Nothing. Both are used interchangeably. Only the tone is sometimes slightly different.
'I guess' can sometimes sound like you are genuinely unsure, so you are agreeing.
Whereas 'I suppose' can sound like you don't want to agree, but you have no other facts to prove your argument, so you are forced to agree.
"Hey is that building over there being demolished??"
(unsure) "I guess!"
"Medical treatments are very unreliable sometimes, because you can't always control the side effects."
(Umm, I don't exactly think so, but I have no proof) "I suppose."
I guess/I suppose is also sometimes used when people don't really care about what you're saying.
"Hey is that new anime coming out this month?!?!! DUDE"
"I guess." (meh I don't really care, yeah whatever)
"God the government is terrible and politics are crazy bla bla bla.."
"I suppose" (yeah yeah okay who cares)
But it's a very mild difference in tone, so it almost doesn't matter at all. It mostly just depends on the way you say it, so it doesn't mean they will always come across in that way so you don't have to worry too much about that. I'm only telling you to give you extra information, but you can use either whenever. :)