Sudoku is definitely the best aspect of Brain Age. In my opinion, Brain Age also has the best console sudoku implementation. That opinion comes from me playing Sudoku Mania! (DS), Go! Sudoku (PSP) and the version in Brain Age. I feel like I'm leaving one out, but oh well.
Sudoku Mania has issues with write detection and cannot detect a '5' using any method (actually writing a five, writing an 'S' which tends to be interpretted as '5', etc). Personally, I love write detection for playing sudoku as you feel like you're actually doing it on paper, so it's either that or nothing.
Go! Sudoku had a horrible "Please Wait!" screen that'd pop-up ever so often and god knows why it did. The worst part was... when this screen popped up, the timer was still going! I didn't mind the no writing part, since this was a PSP game and didn't have the availability of that functionality, but the wait screen sealed the deal for me and I sold it back to EB.
Note that I also sold Sudoku Mania! back to EB as well.
But for BA vs BBA, I'd say if your dad is more of a technical guy, go for BA... if he's more of a visual/hands-on kind of person, go for BBA. BBA also has more of a "kiddie"/cartoony feel to it, so be a bit warned on that.