I think they are both really successful in their own way, you can't really measure success only by album sales because Britney releases an album pretty much every year or every 2 years while Christina usually takes 3 or 4 between each album so just by logic Britney will sell more and be more "popular" because she's seen and heard more often.Regarding the Christina vs Britney debate, yes Christina probably has more range than Britney, but some people prefer softer vocals. Britney is far more successful than Christina and that speaks volumes.
If you want to measure success by awards, Christina takes the prize with multiple Grammys and awards everywhere.
If you want to measure success by voice and recognition of the music industry, Christina takes the cake.
If you wanna talk about success in the movies, Burlesque did pretty good worldwide while Crossroads tanked everywhere.
If you wanna talk about tv success, well The Voice has bigger ratings than The X Factor and the fact that Britney (or her people) decided to join a reality music contest after Christina did it and made it cool speaks volumes (and I didn't say that, The New York Times did, http://www.nytimes.com/2012/09/18/ar...usic.html?_r=0 ).
So there. Success is a very vague concept and, as I said before, they are both successful in their own way.