Both appear identical in the pan, and to be sure, they are from the same colour family - both are muted, everyday, go-with-everything neutral pinks.
L-R: Rock and Republic Spank, Stila Bud
I was curious to see if they were actually dupes or not, so I swatched them side by side. I think they're pretty close, although they're not absolute dupes. But they are close, though, so very close.
L-R: Stila Bud, Rock and Republic Spank
They're pretty much the same, but Spank is a little bit brighter than Bud, and also perhaps a little bit more cool-toned. But they are both muted neutral light pinks, so the similarity is pretty slight. I guess when you actually wear the colours on your cheeks, they're not going to look too different.
Quality-wise, both were good, although the Rock and Republic was more pigmented than the Stila, and also had a smoother texture. I'm not saying the Stila isn't good though, because it is, but Rock and Republic is better.
So which should you get, if you can only get one? Well, given that both colours are relatively close, I'm going to frame this as a quality vs price thing. Rock and Republic has the better quality, but Stila has the cheaper price. Both are good though, so at the end of the day, your choice could end up being decided by your budget.