A broken chain will recoil light a bolt of lightning. I've seen it happen. Wrinkled the hood of a K5 blazer like it was made of cardboard and took the windshield out.
jimmer, using a tow strap likely allowed some 'give' thereby reducing the shock load on your tractor. If you drove away without any unsusual noises, etc, I suspect you are fine.
In regard to chains vs straps I almost always prefer a chain EXCEPT in the scenario you are describing. For pulling a stuck vehicle with another vehicle I consider a snatch strap to be by far the most useful and effective tool. But, 1)it has to be a dedicated snatch strap, not just a plain tow strap and 2) it has to be properly sized and rated for the job and 3) you have to use it properly.
To use it properly, you connect the two vehicles at points without sharp edges that will cut the strap. You then let the strap go slack between the vehicles (NOT coiled or bunched up, just lying slack on the ground). Then the towing vehicle moves forward slowly but steadily, pulling the strap taught. You will feel it strectch, the towing vehicle will come nearly to a stop but you keep the forward motion going and then you will feel the strap recoil a little and the stuck vehicle will literally pop out. This has to be done in a slow and controlled fashion, it really isn't 'snatching' its just using the energy of the stretch strap. Done right, it works better than anything I've ever seen and I've seen a lot of different techniques.
Only problem is, a 25' snatch strap rated for this type of thing is pretty pricey.