Both will have lengthy careers. IMO, Katy will most likely continue slaying Gaga on the charts for a few more years, but when both are in their late 30s and onwards, I think Gaga will be more successful then. She has established herself as a serious musician and a talented live performer, and these traits are more appealing to an older audience than a quick catchy hit song. I'm not implying Katy isn't a serious musician, but she has yet to move away from making radio-friendly bubblegum pop. Those types of artists tend to be disposable.
Katy Perry. The only thing that may slow her down is age, but she will probably be successful in every decade she releases music.
Gaga will never leave the stage, but I think she's going to cease being a pop star. I wouldn't be surprised if she went in a completely different direction. I say this a lot, but I see her with a very successful career on Broadway.