I wouldn't want an R34 GTR.
I had one for six weeks, great car, but your EVO is better as was mine. The GTR's real advantage for me over the EVO was its engine sounded nicer and it was RWD until otherwise needed. But it was just old and running cost were insane, even when driving gently.
As a road car I've said this many times not much will live with an EVO especially if the road is particular bad as in bumpy or if weather conditions are poor etc. An EVO 9 or 10 running 400ish horsepower is a car that will embarrass most cars on the road. My 911 is only faster on roads that are particular smooth or not too bad and for the M3 well it needs a very smooth road and then it might be. The EVO, road conditions irrelevant, weather irrelevant, if you have the confidence to push them, they are very quick on road.
What do I prefer driving on the road? 911 every time, I can drive at 7/10th and feel amazing, or I can wind it up to 9/10th's and pretty much leave anything and still have great enjoyment, point being its a challenge whether I am going just kind of fast and plenty of fun or I can go silly quick and get a sweat on. Plus it sounds ten times better and the communication and feedback a Porsche gives is un-rivalled.
In the EVO I never felt challenged even when driving it at 10/10th's.
On the track different ball game altogether, my EVO would not stand a chance against the 911 even in the wet on track. Against the M3 on track well the M3 is even quicker again, but in the wet, EVO everytime on track, the M3 is poor in the wet, well it was, suspension and tyres now sorted, but my money still be on EVO.
The GTR looks better but both very dated.
