If the anchor rig can back up with the stuck rig attached to it, then forego the winch and just tow or snatch it out. There is really no reason for the non-stuck rig in a winching situation to back up while the winching is going on. Except maybe to reposition (during a break from the actual winch pull).
Never use a winch as an attachment point when towing and NEVER use a winch as an attachment point when snatching.
If the stuck rig is in mud (not hung up on rocks), then gently assisting by applying power to the wheels of the mired rig is the best way to extract it. Power tires try to crawl up and over or at least forward while the winch pulls. No powered tires just act as anchors that the winch has to overpower.
I've had many extractions where there was simply no way to move the rig unless it was also spinning it's tires.
This last fall we had to extract a Unimog from a fairly deep mudhole. It was frame down with a clay bank at each end of the pit. We were pulling with an OEM PTO double lined with an FJ40 and an F350. The bank in back was high enough that even with the tires turning, we were just pulling the mog dead into it and he couldn't climb up. When we re-riged and pulled forward the mog wound up tipped pretty steeply to the side. The 100 gallon fuel tank he had in the rig did not have any internal baffles and in it's half empty condition he sucked air and the engine died. With the engine dead we were trying to plow the tires through and under thick clay mud that was 3/4 and more up the tire. Once the obstruction (mud in this case) is above the halfway point on the tire, it doesn't try to roll even, much less climb. It just pushes through.
With somewhere between 16-20K of pull on the mog it just sat there as the '40 and the F350 were pulled through through the berms/holes that they were anchored in, even with all 8 tires locked and dragging.
We had to rig an alternative flow route for the fuel via a siphon hose and a secondary electric pump... then had to bleed the injectors... then had to use some wd40 (acts like starting fluid in a diesel)... to get it running.
Once the engine was running we could keep the tires spinning and as we winched it forward they climbed up (a tiny bit) and rolled through (a tiny bit more) the muck as we winched. It came right out with this approach.
I've seen many other situations where the only way to get a mired rig out was with it doing it's part to climb while you winch. And I've seen winches burned out due to not taking this approach. In one instance I actually laughed about it a little to myself 'cause it happened to a bit of an ass who refused to listen and insisted on doing it his way instead. What made it funny was that his was the stuck rig and it was his buddy's winch that burned out. The buddy wanted to follow the offered advise but he refused (don't ask why, I have no idea...). He wound up buying a new motor for his buddy because if this.
Mark...