Successful extraction and winching is an art form honed by a lot of practice and application. To the O.P.'s question, I would say it depends. Firstly, I would never try a two rig pull unless it was the last chance at recovery, and never with two straps and no winch. There are too many things that could go wrong. Too many quickly moving and uncoordinated parts. Slow and focused are the parameters: one move at a time and stay safe with audibles. Are there any obstructions that would cause a dead pull? If you could make sure the wheels will roll, or at least the chassis slide, one winch should do the trick with an operator who knows what they are doing. The other not-so-obvious point is always have an equal size rig or larger pull the other out. I remember watching 3 CJ's trying in vain to pull out one H-1 Mil spec hummer. All for naught. Another H-1 came one the scene and, voila!, one extraction completed. Pulling anything with my 15K pound Warn on my empty RAM usually requires a dead man: a means to make the wincher immobile while winching. After having my truck just slide, wheels locked, toward the winchee a few times it was obvious that a dead man was the ticket. To really slow things down and almost double the power, a snatch block is the right tool. But there are caveats. My 15K winch only has 90 feet of 1/2 inch cable so folding it in half gives a max of about 40 feet of pull. My old CJ-8 with the Warn 8274 (fastest winch in the west) had 150 feet of 5/16 wire rope, plenty enough to use a snatch block. Damn, that was a great winch. In 1969 we had 3 chained (tires) up Toyota FJ-40's attempting to get into Domeland (now closed to vehicles) in the Southern Sierra through 3 feet of freshly fallen snow I think around New Years Day. Occasionally, we had all 3 FJ's closed up and pushing each other like a multi unit train engine lashup. Since they all had the same bumper height and stock tires it worked pretty well. In conclusion, I would only use a strap if it were a relatively easy and controlled pull and would not need brute force or a quick pull. Even then, D rings on both ends of a looped, both ends strap that has well over the capacity needed.
jefe