Both of them mean the same thing, which is to express the speaker's opinion about something. The difference is that one is less committal than the other.
Sometimes people don't want to be direct when expressing an opinion. They might not be completely sure that they're right, or they might not want to set themselves up for a confrontation, or they might just not see themselves as someone whose opinion should be taken at face value. They might just have a non-committal personality. For whatever reason, they want to voice an opinion without taking full responsibility for it. In these cases they might say, "I would think that..". The implication is there is some condition that must be met for them to think what they say they would think.
Under normal circumstances I would think that...
If I were an expert I would think that...
If you want to believe what I say I would think that..
If I'm not mistaken I would think that..
It gives them a mental escape in case they happen to be wrong or someone disagrees with them. It's only their opinion if the condition is met.