Rihanna has the bigger career and is currently bigger.

Lady Gaga has the much, much bigger peak and has the potential to come back harder

http://atrl.net/forums/showthread.php?t=372169

And I dont think you even want to discuss Rihannas dominance in UK hunty.

Bye.

Gaga's biggest tour is bigger and more global than Rihanna's biggest tour.
Gaga's biggest single is bigger and more global than Rihanna's biggest single.
Gaga's biggest album is bigger and more global than Rihanna's biggest album.
Rihanna is nearly non-existent in the major Asian markets (you're not global unless you can sell in the major Asian markets).
Gaga has won more awards in more countries.

Most of Rihanna's success comes from a few key areas, such as North America and Europe.