Well no too big difference in spoken E; you just need to figure what "out" and "over" mean respectively, both as prepositions.
This is not a complete comparison:
"Out" is not quite "out", it sounds near actually outside, out doors. The kids are playing out there. Actually "out there" mostly refers to an abstract "location" (usually with somewhat a negative sarcasm, kind of kidding): What are those big guys dealing with everyday out there?
"Over" is real "over", it sounds distant in some cases. eg, you'll say to your abroad friend: How're you doing over there? And "over there" could be interchangeably equal to "out there": Who's the man over there?
One tip: "Outta there" used as an adveb (ie, no verb conjunct with "out" that has a direct relation with it) is often seen and is wrong because "out" is a prep in "out there" where as an adverb in "out of there". Speaking of that, I myself often make the mistake.
They'll get out of there.
What do you do out there. (No direct relation with "do")