They are pretty closely matched but the R9 270X is the stronger card, however I only have a PCIe 2 bus. I believe the R9 would max out a PCie2 bus's Memory bandwidth and the HD7870 is just under. How much would this affect the performance?
Modern graphics card should not saturate a 2.0 x 16 bandwidth. Go with what ever card works best for you. There are several reviews out there which show you really only start to lose a little performance at around 2.0 X 4 and below.
edit -- the 270x is just a rebadged 7870, that is why the performance is so close, I believe they just pumped up the clock frequency on it. I would just grab the cheaper of the two and over clock slightly.