Turfs will give pretty much the same "traction" as R1s - UNLESS/UNTIL they plug up with snow, clay, whatever.
Rubber is rubber, etc.
There are times where wider tires can "bridge" what narrow tires can fall into, which can be the first step towards a rut.
I sometimes want 3 sets, but loaded R4s can take a lot more
ballast than comparable R1s, so I have "better traction" with 55 gallons per tire than 35 - until they load up (-:
I find a set of loaded R4s for Fall, Winter and Spring work out quite well, for me, for what I do, for how I do it.
The Turfs are great for the summer mowing season and I have done quite a bit of dirt work with them when it hasn't been worth swapping back to the R4s for one or two little tasks - that often turn to 6 or 7.
The other dimension of this is "Domestic Bliss", it might dominate all technical considerations.
IOW be pragmatic.