I drive a 1997 Audi A6 wagon with Quattro AWD. Tire wear had been an issue, until I ditched the orig Goodyear Eagles and put Michelin Hydroedge on all 4. Wasdoing great until irreparable nail hit took out 1 front tire on a road trip. Solution? I limped into a dealer on my donut who unfortunatley did not deal Michelin. He did have an H rated W+S all weather Capitol tire with the same aspect ratio (205/R16) although only rate B for temp and 420 for Tread life (vs A and 780). Different tire company - different but similar tread design. Same traction and speed ratings. Did I mention these tires were slightly used? and the approx diameter of my existing Michelins? LSS - At the dealers suggetion I put the Caps on the front, and put the two best Mich’s on the rear. SFSG. Now, though, another one of the Mich’s has a nail in the SW. I go to another tire dealer closer to home who tells me the mismatch in tires I have perpetrated (about 7500 miles worth, is an absolute motoring heresy). I’m lucky, I’m told, to have any surviving AWD components,a transmission that are still answering the call to duty - hair or a 401K plan. I’m thinking - what kind of scare tactic is this? AWD is supposed to sense and differentially apply power to each of the 4 wheels based on actual road conditions. And road and load conditions can vary a lot by wheel where I live (San Francisco) So why would constantly but only marginally different characteristics between front and rear cause the system such unholy trouble. Where’s the evidence? Should I be living life in mortal fear? Dare I now put two new Capitols on the rear (to match the front ones by manufacture - but not treadwear)? Do I have to buy four new tires - Should I sell this lemon? Or no matter what I do, for having listened to the siren song of my wallet (what? buy four new $ tires to atone for one bad expensive 1- are you nuts?) Or am I consigned to the lower rings of AWD induced hell forever?
First, see if there is anything in your owner’s manual about the maximum acceptable variation in circumference between tires. If there isn’t, ask Audi via E-mail without mentioning that you have been driving on mismatched tires.
We have an all-wheel-drive Subaru wagon. According to Subaru, the maximum permissible difference in circumference is 1/4 inch. That corresponds to 1/25 inch of tread wear. Your Audi may or may not be more tolerant.
As far as the differential components are concerned, the circumference is the only thing that matters. Different grades of tires could cause handling problems and traction problems in low traction conditions. I think the latter is not as important in an Audi because of the type of differential they use compared to the type(s) used by everyone else.
The Audi uses, or used to use a differential with specially cut gears that transfer nearly 100% of the power to the wheel with the most traction.
In most differentials, when going forward, the differential gears don’t move, in theory anyway. That is they don’t move relative to the ring gear. They only move when the wheel on one side needs to travel further than the wheel on the other side. If you have tires of a different circumference, then these gears are moving all the time, which wears them out. The center differential is usually a limited slip type which means that clutches have to slip to allow for differences in distance of wheel travel between the front and rear wheels. Again, you don’t want the clutches to slip all the time. But again, I think that Audi uses a different system so this may not be a problem.
Handling would be the big concern here though.
All of our problems are going to get much worse with all the new complicated computer junk being put on the new cars. Stability control is going to be the next unfixable thing. Run flat tires are just getting unpopular. I’ve seen some of the strange directional tires that cost way too much. Antilock brakes are nothing but a nuisance. They cause power brakes to be hard to operate and maintain. I had a 79 Chevy pickup that was the best stopping machine on snow without power brakes. I had an extra cab Mazda that stopped so quick on dry road that it would scare you. Nothing special or AWD about those. If anything good is invented, there won’t be room in the car for it. I wish us all luck in the future. We will need it.
Yes, by trying to make everything safer, they’ve complicated everything to the point that we’re not so far off from having cars that will drive themselves(the radar cruise control is just the begining 
), we’ll simply own them and go along for the ride. If it ever comes to that, I’m sure there will be those of us who, even if mandated by the gov’t, will still own and operate a normal car