It doesn't matter who was bigger in any given time the fact of the matter is one is still going strong 15 years in her career while the other is on her way out barely half a decade into her career.
Gaga's peak in 2009/2010 alone was the 2nd biggest for a female ever behind Britney but overall Bey scored 3 successful eras in that time and maintained it longer so I'll pick Bey.
But really though Beyonce was huge too.