Rotating mass has to over come a lot of inertia to speed up or slow down. So it matters a lot.
However, I doubt a Duratrac is lighter than a Cooper AT3. If anything, the AT3 is probably lighter. Unfortuneately I can't find any info about AT3 weight. So we can only guess.
My local tire store sells Duratrac and Cooper AT3. I suppose I could bring a scale and weigh them. Any of you could do the same. Any volunteers? I already went to tire store and photographed new version Grabber AT2 for a couple guys in another thread. If I go back again with scale, the tire store guys will think I'm nuts.
Tread pattern, compound, and amount of sipes affect rolling resistance. Rolling resistance affects gas mileage. Cooper AT3 is less knobby tread and has silica in tread compound - both decrease rolling resistance.
I don't think tire aerodynamics matters much, but to whatever extent it matters, the AT3 obviously has less aerodynamic drag than Duratrac. Look at the treads.
Common sense tells me a Cooper AT3 will get better gas mileage, be quieter, and smoother riding.
The Duratrac in a C-rating version is 44 pounds whereas the AT3 (also C-rated LT version) is 50 pounds (both in my size, 265/70/17). I bet the AT3 is less noisy and has less rolling resistance and has pretty much everything else going for it over the Duratrac in terms of fuel efficiency, but the Duratrac is light, that's for sure. The AT3 still may get better mileage because it's just a lot less aggressive.
The AT3 is a great tire, I'm sure. I just don't care too much for the way it looks (I especially wish it had some sidewall "tread" like the Duratrac or even the Nitto Terra Grappler and Toyo Open Country ATII). It has average tread depth for an AT (16/32s) and the tread just isn't very aggressive. The Two best looking AT's in my opinion are the Duratrac, with looks almost like an MT, including the aggressive sidewalls and tread depth that's almost as deep as an MT (18/32s) as well as the Cooper ST MAXX, which also has equally deep tread and decent sidewall lugs. The only problem with the ST MAXX is that it only comes in an E-rating and is 55 pounds in 265/70/17. I really wanted the ST MAXX but the Duratrac is a lot lighter.
For me, right now it's between the Duratrac and the Toyo Open Country ATII. I'm confident the ATII will be a great tire and should be very quiet, better on gas, etc. It's almost like what I wanted the AT3 to be. Better looking/more aggressive tread with sidewall "lugs" (and I like how the lettering isn't white). However, the only problem is you have to get an LT version to get the 16/32 tread depth and the more aggressive sidewall lugs. The passenger rated version, which is very light and soft riding has shallower tread and milder sidewalls. And the only problem with that is it only comes in an E-rated version. So I'm slightly worried about stiff ride but I'm thinking it shouldn't be too bad for an E-rated tire because it's still only 48 pounds in an E (lighter than a C-rated Cooper AT3). On the other hand is the Duratrac. I love the looks and it's supposed to be fairly quiet for how aggressive it is and it's light. It probably won't get quite as good of mileage as the Toyo but it has deeper tread and probably does a little better off-road, which could make up for that. However, I've heard it's hard to get balanced correctly and the sidewalls are weak (at least for rock crawling, which isn't a big deal to me). I'm toying with the idea of getting an E-rated Duratrac because it might solve all of the issues people seem to have with them, which is probably mostly with the C-rated version. The E-version would be heavier duty and should be less likely to puncture. I also have a feeling it will be easier to balance with it's extra weight. It still only weighs 50 pounds and I've heard that it rides nicely on my Jeep (WJ) model in the E-version because the part of how they keep the weight down on Duratracs is the weaker sidewalls, so they ride soft. The E version should still ride fairly soft, yet might be less prone to flats and easier to balance. These are just my thoughts and feelings, though. I'm not an expert and I don't know if any of this is true or makes sense. Maybe the E is just as prone to the "issues" and I'd be better of with the C version for a softer ride and better gas. But if it can't be balanced right or gets flats constantly during normal daily driving, then that's not okay. So I'm a bit torn.