Hi Ian,
It's a tough one really as there's no real comparison. While they're both shooting the same pills, they're completely different setups. The Rem is the heavy barrelled police model and I use it as my project rifle, the one I pour my cash into and shoot at the range. The Tikka on the other hand is my workhorse; she's the one I drag through the mountains in NZ running after Tahr. They both shoot extremely well for what they're used for.
At the moment I have the Rem in a AICS stock, it's got Barger Ordnance rings, 20MOA rail and bolt knob and a Leupold Mk4 6.5-20x50 IR scope on the top. The Tikka on the other hand is stock with a Leupold VX-1 3-9 on the top, but for a stock rifle she's amazing - those Fins sure know how to build a lovely rifle.
Cheers,
JJ.