The Golf R uses an EA113 2.0T - like Mk5 GTI. The Mk6 GTI is based on the new EA888 platform. The newer motor has upgraded pistons, rings, new oil/fuel/vacuum pumps, a new MAF and is chain-driven. It's more fuel efficient, has lower emissions and a lower compression ratio.
It's probably possible to swap turbos, but not straightforward. Wait for AWE's K04.