I've accepted an answer in 2010. In 2011 new options came to hand, and a better answer was posted. Should I move the accepted answer to the new one?
Is it a better answer than the one you previously accepted? If so, yes.
There is nothing wrong with changing the accepted answer when a new one comes along. That's part of what differentiates Stack Exchange sites from traditional forums, where questions that have been answered are effectively "closed" and no one ever contributes new information. Since that leads to stagnation of old questions and inflation by way of new duplicates, we try to avoid it. Instead, users are encouraged to seek out existing questions and post better answers. Rewarding those users' efforts by changing the accepted answer is quite commonplace.
Remember that while you can only accept a single answer, you can and should upvote all of those that you find useful!
If you find the new one more useful to you, then there's nothing wrong with changing the accepted answer to the new one.
It would be nice to open the change of accepted answer to the community (restricted to those with a certain minimum reputation) in situations where the question asker is no longer active. Say, when a ratio of 5:1 community votes outnumber the accepted answer...