Like with anything else, it depends on the woman. I sometimes dated older women when I was younger, and I tend to date women my age or younger women now. That's not so much on purpose... just how things have worked out as I meet people. I just don't think you can generalize. The older woman should have more life experience than the younger woman, but that doesn't mean that she's any wiser.
The only pattern I've picked up on is with women in their mid 30's who don't have kids yet (and want kids). I've sometimes felt like I was being interviewed as potential husband or daddy material - and I have no immediate plans to be either. But with this woman being 51, that's not likely to be something you'll deal with.
You just have to get to know her. See if you have shared interests. Don't go in with preconceived notions about what she'll be like, just because of her age. And good luck! :thumbsup: