I did not know this.  I just figured both go to Hell, so both suffer.  Can you provide Church teaching on this?

11.

(. . .)

The reprobate then shall hate and curse all the benefits which God has bestowed upon them. They shall hate the benefits of creation, redemption, and the sacraments. But they shall hate in a particular manner the sacrament of baptism, by which they have, on account of their sins, been made more guilty in the sight of God; the sacrament of penance, by which, if they wished, they could have so easily saved their souls; and, above all, the most holy sacrament of the altar, in which God had given himself entirely to them. They shall consequently hate all the other means which have been helps to their salvation. Hence, they shall hate and curse all the angels and saints. But they shall curse particularly their guardian angels their special advocates and, above all, the divine mother Mary. They shall curse the three divine persons the Father, the Son, and the Holy Spirit; but particularly Jesus Christ, the Incarnate Word, who suffered so much, and died for their salvation. They shall curse the wounds of Jesus Christ, the blood of Jesus Christ, and the death of Jesus Christ. Behold the end to which accursed sin leads the souls which Jesus Christ has dearly bought.

All these things which we have considered are well calculated to make comprehensible to us the priceless privilege of belonging to the Catholic Church, a blessing which we can never sufficiently appreciate, a grace which has been imparted to us by the mercy of God without any merit whatever on our part. He who has the misfortune of being born and taught in a false religion may turn to the true one, and many have done so. Yet it is extremely difficult to overcome the prejudices of training and education. Hence let us be most grateful to God for the precious gift of faith, and let us make use of it in the way He desires. Without this the blessing will be not only useless, but will merit for us greater punishment. What would it avail us, indeed, to be children of a holy Church if we were to lead lives in contradiction to her teachings?

538.

(. . .)

Among the obscure caverns of the infernal prisons was a very large one, arranged for more horrible chastisements than the others, and which was still unoccupied; for the demons had been unable to cast any soul into it, although their cruelty had induced them to attempt it many times from the time of Cain unto that day. All hell had remained astonished at the failure of these attempts, being entirely ignorant of the mystery, until the arrival of the soul of Judas, which they readily succeeded in hurling and burying in this prison never before occupied by any of the damned. The secret of it was, that this cavern of greater torments and fiercer fires of hell, from the creation of the world, had been destined for those, who, after having received Baptism, would damn themselves by the neglect of the Sacraments, the doctrines, the Passion and Death of the Savior, and the intercession of his most holy Mother. As Judas had been the first one who had so signally participated in these blessings, and as he had so fearfully misused them, he was also the first to suffer the torments of this place, prepared for him and his imitators and followers.

751.

(. . .)

Then and there the infernal spirits resolved to persecute and torment more grievously the Catholics, and chastise more severely those who should deny or repudiate the Catholic faith. For they concluded that these merited greater punishment than the infidels, to whom it is not preached.

9.

(. . .)

And what I just now said, that I repeat, that they shall suffer greater punishment, who, when they have enjoyed all good things, do not even so become better. For all shall not be punished alike; but they who, even after His benefits, have continued evil, shall suffer a greater punishment, while they who after poverty [have done this] not so. And that this is true, hear what He says to David, "Did I not give you all your master's goods?" 2 Samuel 12:8 Whenever then you see a young man that has received a paternal inheritance without labor and continues wicked, be assured that his punishment is increased and the vengeance is made more intense.  Let us not then emulate these; but if any man has succeeded to virtue, if any man has obtained spiritual wealth, [him let us emulate]. For (it is said) "Woe to them that trust in their riches" cf.Psalm 49:6: "Blessed are they that fear the Lord." Psalm 128:1 To which of these, tell me, would you belong? Doubtless to those who are pronounced blessed. Therefore emulate these, not the other, that you also may obtain the good things which are laid up for them. Which may we all obtain, in Christ Jesus our Lord, with whom to the Father be glory together with the Holy Ghost, now and for ever, and world without end. Amen.

Would you see those also punished, who were of the number of believers, and who held fast to God, but were not of upright life? Hear Paul saying, "Neither let us commit fornication, as some of them committed, and fell in one day three and twenty thousand. Neither let us murmur, as some of them murmured, and perished by the destroyer. Neither let us tempt Christ, as some of them tempted, and perished by the serpents." 1 Corinthians 10:8-10 And if fornication, and if murmuring had such power, what will not be the effect of our sins? And if you dost not now pay the penalty, do not wonder. For they knew not of a hell, therefore they were visited with punishments following close at their heels. But you, whatever sins thou commit, though you should escape present penalty, will pay for it all There.

Did he so punish those who were nearly in the state of children, and who did not sin so greatly — and will He spare us? It would not be reasonable. For if we commit the same sins with them, we shall deserve a greater punishment than they did.  Wherefore? Because we have enjoyed more grace. But when our offenses are numerous, and more heinous than theirs, what vengeance shall we not undergo? They — and let no one think I say it as admiring them, or excusing them; far be it: for when God punishes, he who passes a contrary sentence, does it at the suggestion of the devil; I say this therefore, not praising them nor excusing them, but showing our wickedness— they therefore, although they murmured, were, however, traveling a wilderness road: but we murmur though we have a country, and are in our own houses. They, although they committed fornication, yet it was just after they came out of the evils of Egypt, and had hardly heard of such a law. But we do it, having previously received from our forefathers the doctrine of salvation, so that we are deserving of greater punishment.

As if then we were banquetting with Christ Himself, and partaking of His table, let us do nothing at random, but let us pass our time in fastings, and prayers, and much sobriety of mind. For if a man who is destined to enter upon some temporal government, prepares himself all his life long, and that he may obtain some dignity, lays out his money, spends his time, and submits to endless troubles; what shall we deserve, who draw near to the kingdom of heaven with such negligence, and both show no earnestness before we have received, and after having received are again negligent? Nay, this is the very reason why we are negligent after having received, that we did not watch before we had received.

Therefore many, after they have received, immediately have returned to their former vomit, and have become more wicked, and drawn upon themselves a more severe punishment; when having been delivered from their former sins, herein they have more grievously provoked the Judge, that having been delivered from so great a disease, still they did not learn sobriety, but that has happened unto them, which Christ threatened to the paralytic man, saying, "Behold you are made whole: sin no more, lest a worse thing come unto you" John 5:14: and which He also predicted of the Jews, that "the last state shall be worse than the first." Matthew 12:45 For if, says He, showing that by their ingratitude they should bring upon them the worst of evils, "if I had not come, and spoken unto them, they had not had sin" John 15:22; so that the guilt of sins committed after these benefits is doubled and quadrupled, in that, after the honour put upon us, we show ourselves ungrateful and wicked. And the Laver of Baptism helps not a whit to procure for us a milder punishment.

And consider: a man has gotten grievous sins by committing murder or adultery, or some other crime: these were remitted through Baptism. For there is no sin, no impiety, which does not yield and give place to this gift; for the Grace is Divine. A man has again committed adultery and murder; the former adultery is indeed done away, the murder forgiven, and not brought up again to his charge, "for the gifts and calling of God are without repentance" Romans 11:29; but for those committed after Baptism he suffers a punishment as great as he would if both the former sins were brought up again, and many worse than these. For the guilt is no longer simply equal, but doubled and tripled. Look: in proof that the penalty of these sins is greater, hear what St. Paul says: "He that despised Moses' law died without mercy, under two or three witnesses: of how much sorer punishment, suppose ye, shall he be thought worthy, who has trodden under foot the Son of God, and has counted the blood of the covenant an unholy thing, and has done despite unto the Spirit of grace?" Hebrews 10:28-29

I'm not following.  How is keeping him from baptism saving him from additional suffering?

I just saw this and thanks trad123 for your references.

11. For He that "did burst asunder the sea and made them go through, did confine the waters as it were in bottles" Psalm 77:13, in order that the water might stand up first as if it were shut in, is able by His grace to restrain the flowing and ebbing tides of carnal desires, when we renounce this world, so that all sins having been thoroughly washed away, as if they were enemies, the people of the faithful may be made to pass through by means of the Sacrament of Baptism. He that "led them home in the cloud of the day, and in the whole of the night in the illumination of fire" Psalm 77:14, is able also spiritually to direct goings if faith cries to Him, "Direct my goings after Your word." Of Whom in another place is said, "For Himself shall make your courses right, and shall prolong your goings in peace" through Jesus Christ our Lord, whose Sacrament in this world, as it were in the day, is manifest in the flesh, as if in a cloud; but in the Judgment it will be manifest like as in a terror by night; for then there will be a great tribulation of the world like as it were fire, and it shall shine for the just and shall burn for the unjust.