Will either of those tire sizes fit my '01 ram 4x4 quad without rubbing at all?

 

either should fit w/o rubbing on stock wheels.
if you change wheels, check your backspacing !!!

however - people with 2wd report rubbing, and every once in a while some 4wd people report rubbing (i think on the suspension arms but not sure).

mine don't rub, but are pretty close.
check the dimensions of your tire, and make sure they're in that 32 inch diameter range. if in doubt, mount up 1 and check it.

edit - here's a couple guys with problems, possibly caused by their lift kit.
https://dodgeforum.com/forum/2nd-gen...ing-limit.html

 

I run 285/75 R16s on my stock wheels and mine rub occasionally on the suspension arms. You just learn where the limit is.

 

I'm running 285 70 17 Terra Grapplers and they rub at full lock on the mud flaps. Truck is 97 Ram 2500 4X4 HD with stock suspension, minus upgraded shocks... If anything maybe consider 275 size, their are a couple brands that make that size, including the BFG A/T Ko's

 

i have 315.75.16 m/t on my 01 4x4 with stock wheels and i only rub when i make tight turns to the left.

 

285/75r16 on 16x10's they only rub on the plastic fender skirt when its cocked up on sumthing and u have the wheels cut... but its not a major rub... like a small spot the size of ur palm

rubs the dirt off lol

 

i have a 285 75 16 and the only rub on the passenger side supspension arms for some reason but only at full lock and its not really that bad