Bar tires are the most aggressive tread and generally narrower. They should get the most traction in tough conditions. R4 is kind of best of both worlds; good still aggressive tread, but not doing too much damage to areas you don't want mucked up, which is why I got them. I had them on my L3800 and loved them. That is why I got them on this BX.
Now however, having owned this and put about 35 hours on it with a lot of mowing at both properties, I think I would go back and get turfs if I had it to do over. R4's are more aggressive to get stuck less and theoretically put more power to the ground, but with this being a used to mow my real lawn as well, if the ground is soft from a recent rain, I do leave impressions with the weight of this thing. I don't have a golf course lawn, so it's not too big of a deal and the R4's are great, but the turfs may have been easier on my lawn in the long run and I believe with the weight of the machine that they'd still be good enough for loader and other ground engaging work like tilling or box blade. I truly don't know though and this is only an opinion.