Brain Age is slow to impress, but opens up a lot as you start to play it more and more. The game feels well grounded in research, and in general the puzzles get plenty hard fast enough. The game does a very good job of introducing random elements into it, and even though multiple people don't play it at the same time, it brings data from other people playing Brain Age into the sessions. For example, when I finished the math quiz today it told me that Tammy did a better job than I did. This resulted in me doing the quiz over and over until I beat her of course. Great encouragement.
One of the really fun things about Brain Age is it's use of voice recognition. Some of the puzzles require you to speak to identify things and it does a good job of interpreting you. Last, the included Sudoku game is very well done. All in, this is a lot of fun.
Big Brain Academy
Big Brain Academy is more game-like than Brain Age. The characters are almost goofy looking, and the games seem more like parlour tricks than well researched logic tests. However, it is a lot of fun as well. It allows multiple player profiles, but doesn't tie them together in anyway to create competition. It doesn't use handwriting recognition or speech. The puzzles do get very difficult and it is certainly taxing, but not as well executed as Brain Age.
The winner is...
Honestly, if you like puzzles, get both. They are different enough that they are both worth having. However, Brain Age is definitely superior in almost all dimensions -- even without the Sudoku game.