They both push when driven at a moderate pace, even the Evo. Once you increase the pace, supposedly, the Evo neutrals out very nicely, and while the R does too, it still won't match the Evo as a pure driving tool. Every single test since the Evo came out, has said its the sharpest, most responsive, and fastest car of the 3 (evo, sti and R variants), but also the least livable, the cheapest quality, and the loudest. The STI is more of a middle ground between the 2 I would say, more "true" awd system, nicer middle of the pack interior, yet has the performance. The R gets the same performance as the STI around the track, but loses in straight line acceleration, has the best interior by a mile, and for me is the best choice.
Totally different cars. If you don't value what a german car has to offer, then you won't "get" the R.
All 3 are great cars.