I am gonna ask my girlfriend for 1 of them, should I just ask for 2 or would it be better to ask for 1? What is the difference?

One of the games has the word "more" in it.

The difference is 1.

Both have 100 Sudoku puzzles.

Brain Age 2 has, arguably, more challenging 'games'.

Plus, you get Dr. Mario with the game(Virus Buster), which adds more replay value than the original.

I own both. Brain Age 2 is a better deal.

Also, consider getting Picross DS. Best $20 you'll ever spend on the DS(Download new puzzles, create/share puzzles over wifi, 345+ puzzles included)

I believe they have different mini games so there is no overlap between the two titles. Either one is a good choice, though BA2 may have a few extra features.

BA2 is better.