There is definitely a major difference in someone telling you that their problems are worse and expressing compassion because you can relate.
There is a saying that goes "misery loves company".
I think that some see hearing another's hardships as an opportunity to share their misery.
Understand that as someone that wants to share the liberty of Jesus Christ, there is a desire to be compassionate towards others and the afflictions that they suffer. However, I can tell you from experience that there are some that would rather remain in their misery than receive hope or freedom. I have wondered why this is. What causes this?
Having a good deal of experience with addicts, I see a huge similarity. Addicts are constantly searching after that initial "high" that they experienced despite the fact that they will never achieve it no matter how hard they try. It is said that they experience a euphoria that they begin to confuse with "love" and that is what they are constantly chasing after. I have noticed that those that seem to find comfort in being a victim also are trying to experience a feeling they have had before. Maybe it was the reassurance or attention that someone gave them. Whatever the case, it seems like they are trapped in a place of misery constantly looking for that "high" of being coddled, comforted, reassured, etc...
I think the two have one commonality; the desire to feel love. It is sad that they can't experience pure love because of chasing after a counterfeit of it and thus continue in an unhealthy pattern.
If we have shared the truth with them and they seem to have rejected it, we need to let go and leave things up to the Holy Spirit.
The best thing we can do is pray that God show them the truth so that they can be set free. This goes for any kind of unhealthy habitual behavior that one may have learned.