I have both and like both.
My fiance and I both thought that Big Brain Academy had more "fun" activities but it felt less scientific than Brain Age. Some people believe that the idea these brain games actually help you is BS, but if one of them did it would have been Brain Age. Brain Age has a ton of Sudoku puzzles built in, if she likes that kind of thing.
My suggestion would be to get them both. I think they retail for $20 and if you're a thrifty shopper I'm' sure you can get them for $15 or less for each. There have been a bunch of other brain games that have come out more recently than those two, I think one was called "Brain Wave", maybe? I never looked into those, but maybe you'd be interested in looking at reviews of the others, too.