This in general depends on what you import into your notion of proof.
I'll give a couple of examples below:
(a) from math: given a typical background logic, it is not really easier to prove or disprove any given proposition. For example, it is not clear that disproving P = NP, or Goldbachs, is easier than proving it. More generally, by Godels incompleteness theorems, we have that there exist undecidable sentences in any reasonable theory- sentences that cannot be proved or disproved.
(b)from science: one can construe a naive popperian view. Suppose for example that we have a theory T, and some experiment E and we have that T predicts not E. We have just falsfied T, hence disproved it. On the other hand, for a naive verificationist, suppose we have some theory T', experiment E', and T' predicts E'. Then, we have just verified T'. Under these views (first passes!), it is easier to prove something wrong than to prove it right. Of course, Popper's original criticism was that this verification does not constitute a proof of T'. However, adopting a more sophisticated view- such as holism- allows us to modify the background theory T in response to evidence, making it equally hard to inductively show whether T was ever "right" or "wrong" in the first place. Of course, this is all assuming scientific realism (although a similar argument could be made for the instrumentalist but not the anti-realist, likely).
(c): decisions- OP mentions choice. Now, it is possible to be in a game in which you have far more "right" choices. Consider for example when one reaches the tipping point in a game such as chess or go. So long as one doesn't fumble spectacularly, most choices will lead to a win state (and one can prove so, presumably, although such a proof would be beyond our current computational powers).
The upshot of the above is that proof is not in general harder than disproof. Further, it is not clearly the case that there are always more wrong answers than right answers (since, given LEM + bivalence, we can, of any question of form : "P(x)?" we can ask "~P(x)?"). But this is wandering off track.