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Saying they are both "in hell" is an over-generalization.  That's like saying a person sitting on the beach in sunny Florida and a person freezing to death in a Siberian prison are both in similar situations "on earth".  We know that Heaven is a vast, vast place with different levels and glories, as each level gets closer to God.  Hell is probably similar. 

Yeah, this part just doesn't seem to sink in here.  "Hell" can refer to hell of the damned or else to Limbo (as it does in the Apostles Creed).  Church has not technically defined Limbus Infantium, just rejected the Jansenist assertion that it's Pelagian.  So one can claim that infants burn in Hell if they like, but St. Thomas had it right.  As for Limbus Patrum being a difference "place" from Limbus Infantium, there's absolutely no Church teaching on the matter.  Could very well be the same place, just with different occupants at different times.  In fact, there are a minority of theologians (who have not been condemned) who claim that Hell isn't a specific place but can be anywhere and everywhere.  There's very little the Church has defined on the matter.

We know there's an eternal Heaven.
We know there's a Purgatory that will go away at the end of the world.
We know there's an eternal Hell of torments for the reprobate, where each individual suffers in proportion to his sins (that's part of one dogmatic EENS definition).
We know there was a Limbus Patrum in which the OT just resided until they were liberated into Heaven by Our Lord's descent there.

Beyond this, there are a variety of opinions.  St. Augustine and a few modern holdouts believed that infants who died without Baptism went to the Hell of suffering.  St. Thomas thought that there is a Limbus Infantium where there's perfect natural happiness (I agree with him).  Then there's speculation about a lot of other matters.  We saw Dante putting "noble pagans" in Limbo (I agree with him on that also).  St. Ambrose wrote of martyrs who died without Baptism as "washed but not crowned", where they could not enter the Kingdom but were somehow washed.  Do these go to Hell proper or do they go to Limbo?  Or are they actually baptized invisibly by angels (per St. Cyprian for instance).  If, as per St. Thomas, God would send an angel to enlighten infidels, can't this same angel also baptize them?  Theologians after Trent (like Cano) wrote of infidels who could be justified, but not saved.  Where do they go when they die?  There are so many open questions beyond those few points above that are simply not defined.  And BoD is actually in this same category of speculations.  There's no evidence it was revealed.  For 700+ years, with the exception of some Jansenists, nearly every theologian believed in the Limbus Infantium described by St. Thomas.  And yet the Church has not stepped in to positively defined Limbus Infantium as Catholic doctrine, and it's not considered error to cling to St. Augustine's opinion ... unless you also hold that Limbo is Pelagian (which was condemned by the Church).

Lad even went so far as in his criticism to say that the deprivation of the beatific vision was not a "penalty," when an authority no less than Innocent III said it was exactly that, a "penalty."

You keep demonstrating how ignorant you are on the matter.  It isn't just what I say.  St. Gregory nαzιanzen and a couple of other Eastern Fathers stated exactly this, and St. Thomas' articulation of Limbo made the same point, that ELEVATION to the supernatural life is a free gift, owed to no one, not necessary for the perfection, and therefore perfect happiness, of created nature.  Withholding a free gift is not a penalty in any real sense, but only in perhaps a relative sense.  As for Innocent III, he also wrote at one point that Mass was valid if the priest merely thought the words of consecration, an opinion for which St. Thomas rightly excoriated him.  This is not merely my opinion, but is founded in the Church Fathers and sound theology regarding the natural vs. supernatural states, as expounded by St. Thomas Aquinas.  So your reducing it to "Lad"'s opinion simply means that you're completely ignorant about the matter, he who asserted the (objective) heresy that the water of Baptism is a metaphor for Christ.

Take up your argument with St. Thomas.  He was the one who taught that deprivation of the vision of God is not a punishment.

Is this from the Summa or another work?