I don't think we suffer more or less than others, we just know what to do with it (offer it in union with Christ's sufferings on the Cross) and that is a huge advantage. I don't know what sources you are referring to, it would probably help if I knew the context of that thought, because it could change everything.

My thoughts off the top of my head are that I'd almost say that we suffer less, because unholy living makes life miserable. People who live in sin are not happy. Sin is only conducive to disorder and discord and more sin, whereas the Catholic who lives his life with a clean conscience according to God's Will is a person at peace.

This does not mean that the Catholic does not suffer and goes through life like a breeze, we suffer tremendously as well and sometimes more as victim souls to gain grace for sinners, it just means that at least knowing how to use it to our sanctification is a source for peace and joy that is unknown to the world.
 

If one is more sensitive to things, the suffering is greater.

For example, Christ's body was perfect.  His extreme sensitivity would have made His sufferings greater.  His soul was perfect, too -- he knew the evil of sin as no one else can.  Therefore, it caused Him greater sadness, disgust, etc.  Much the same can be said about Our Lady, whose body and soul were were so beautiful and functioned so perfectly.

Similarly, Catholics SHOULD suffer more than others, in the sense that we SHOULD see reality much more clearly (that we do not is our own fault).  The Saints suffered greatly precisely because their vision of themselves and the world had been so purified that they better appreciated the seriousness of evils of every kind, whether material or spiritual.

The reason I believe that men that are Catholic suffer than other men, is because of their acute awareness of the filthy world around them. They constantly have to guard their senses against demonic attack (i.e. filthy images, bad music, pressures from peers to drink and do drugs, sɛҳuąƖ references and jokes among people at work, et cetera).

The world for a Catholic man is riddled with traps, and sometimes they are veiled so that they look rather harmless. A good thing to read would be Saint John Bosco's account of the road to hell. Here, he is speaking to Catholic boys as to how easy it is to fall into traps, and how you must guard your footsteps.

For a protestant, or a heathen, or a pagan, or any other heretic or apostate, there is very little suffering in terms of -true- suffering. Material suffering is, granted, painful to the senses in a real sense, but suffering in terms of spiritual suffering is the hidden suffering that most real Catholic men endure nowdays.

I don't happen to endorse this website, however, the story is there in its entirety.

http://www.todayscatholicworld.com/bosco_hell.htm

  Yesterday was a holiday (qadr night) so we went to a vila in a nearby city. We could not buy bread, though we had some food with us. As it was both a lamentation day and ramadan, almost all stores were closed, and one must not eat or smoke in the pubilc in this month. I was in the car and had to lower my head in order to eat (we found some open store at last!). when we reached the vila, we could not sleep as lamentation groups were making a loud noise outdoors by their cries, chantings, and prayers. It continued till 4 am.
  Now someone objects to fish fridays and one hour fasting before the Eucharist.....