I think both of those would be fine for running LoL, but the R9 270 definitely would be. It's capable of running BF4 on high @ over 50 fps, so it shouldn't have a problem running LoL at 60.
I have R9 270x, i5 3550p and 8gb ram and I'm getting 170-200 fps in LoL everything maxed 1080p. I can even run Bioshock infinite at 80 fps with max settings. R9 270x is just an overclocked r9 270 so it can run almost all games just as well.