I'd go Winchester, but either Featherweight or Extreme Weather. Either would be cheaper, or about the same price as the Remington.
In standard rounds you get 5+1 rounds in the Winchester instead of 4+1 in the Remington.
Winchester has a steel floorplate vs aluminum.
Remington traditionally has had better triggers and usually better accuracy, but if going with the new FN produced Winchesters it is about a draw.
The bolt handle does not lock down on the Remington. It is possible for your bolt handle to catch on brush and open, dumping your chambered round on the ground.
I like the 3 position Winchester safety better, but like the position and operation of the Remington better.
Remington bolt handles are soldered on vs made as part of the bolt on the Winchester. Although rare, the Remington bolt handles do sometimes fall off.
Quality and workmanship appear to be about equal in my experience.
Most guys don't really understand the purpose of CRF. Unless there is something wrong with either the ammo or rifle, either will feed into the chamber equally well. In any position, even upside down. The CRF offers much more foolproof EXTRACTION and EJECTION. Especially if you somehow allow dirt, ice, or snow to get into your action. Sometimes this cannot be prevented in a hunting situation.
While I may never need it. I see no downside to having CRF. If everything else is equal I prefer it, but it would not stop me from buying a pushfeed rifle if I otherwise liked it.