The GBA could play original GB Operation C, which was pretty good, and GB Alien Wars, which I never tried. It can also play Contra Advanced: The Alien Wars EX which is pretty bad. Even though a Contra III that replaces the overhead levels with stages from Hard Corps sounds good in theory, in practice it kind of plays like shit.
Contra 4 on the DS is a legit new game, and entirely original. I say go for that.