IMO as long as the timestamps indicate the lower-information answer as a "fastest gun in the west"-type thing and it is not an unattributed copy-paste, it should be left alone to its own democratic fate by the community (votes) and the questioner (accept).
If the answer came in more than a few minutes - say 20-30 -- later, to me it shows that the poster more than likely did not read the existing more complete answer or simply ignored it. In that case, I would downvote it with a comment indicating why, and recommending either a self-delete, or a more extensive edit (adding unique information) to cure the downvote.
As Eliah mentions, there certainly are cases where such later-and-with-less-information answers get upvoted more and sometimes even accepted. I think those should still be left alone, trusting the law of averages and a somewhat intelligent reader who will return to read the alternatives if the accepted/most-upvotes answer doesn't do the job. I would certainly upvote the more informative answer(s) though -- as I usually do anyway -- while not voting on the later-with-less answer.
For new answerers who might get agitated in the above situation when theirs is the older answer -- as I was a while ago -- here's a reassuring example of democracy in action in a somewhat similar situation. Note that the answer was initially unaccepted, got Populist and then seems to have even convinced the OP to change his mind and switch his accept.
