Britney definatly, her peak was one of the best of all time, in 50 years people will still remember BOMT where I don't think people will remember Pokerface..
I like them both but Britney, definitely. Gaga has only been around a few years so it's not really a great comparison (although, that being said, her "downfall" did come before Britney's did).
I never experienced Britney's peak. I only found out that she had a backlash like a year ago when i started browsing here. A mess. So i'm not fit for the question. Although according to the OP Britney's peak lasted 12 years and gaga's 5. So with the information provided, common sense would tell the OP its Britney. Unless, of course, the OP thinks in those 5 years gaga may have had triple the impact Britney had.