Accept the one that you found more helpful; that's really the only criterion for acceptance. But if you really can't decide between them, then you have at least four more options:
Accept neither. That's perfectly acceptable, and we will forgive you. Although the checkmark is a nice thing to see on one of your answers, the benefits it provides are small compared to getting lots of upvotes.
Nudge them both to incorporate information from the other answer, then accept the first that does. It's sometimes seen as "bad form" to use information from other answers in your own, but there are no rules against doing so (though courtesy demands at least acknowledging the original source).
Personally I'm not sure I like this option, largely because it creates a sense of urgency that I'm opposed to
Create a new answer incorporating information from both. Self-accepting is explicitly encouraged on the SE network, and our goal is to provide the best possible resource for science fiction and fantasy information. Posting your own answer including the (correct) information from both of the other answers, and then accepting it, is a fair compromise.
If you're worried about poaching reputation or upvotes, you can make the answer Community Wiki, which means you won't earn reputation from it (and you won't earn badges from it). Self-accepts are also not pinned to the top of the answers list (unlike accepted answer from someone else), so accepting your answer won't obscure the other answers unless yours gets more upvotes.
Accept one, give the other a bounty.1 The main problem here is that the awards are radically different; acceptance gives the answerer a +15 rep gain, but the minimum bounty amount is 50. But if one answer is substantially more impressive, while perhaps not answering the question as effectively, this can be a good option
Also don't forget that you can change your acceptance later. So if you choose one today, and then tomorrow the other improves their answer enough that you want it to have the tick, you can do that.
1 Thanks to DVK for returning from exile (briefly) to suggest this