Here's my $.02 from my own logging/towing/rescue experience:
Chain, cable, and straps all have their place. I attended a training session for firefighters put on by our state operating engineers (heavy equipment operators) union training center, the basis of which was giving us an understanding of working with rigging and cranes on structural collapse rescues. The instructor spent a great deal of time covering choosing the correct rigging for the lift at hand, and emphasized that there are often multiple ways to rig a load safely.
With that said, my personal preference is for chain and straps. For most of my lifting, towing, and logging, I use 20' 5/16" grade 70 chains with grab hooks on both ends. With my truck or tractor I'll lose traction long before I even approach breaking strength, and my loader, rated for 1000#, won't get anywhere close to the 4700# rated strength of the chain.
Straps are especially handy for vehicle recovery. They are light, store easily, and are a lot less likely to ding up the vehicle you're working with. The slight amount of stretch in many straps helps absorb the shock load if you take out the slack too quickly or have to "bump" a stuck vehicle to get it moving. The slack does have a downside, as I discovered years ago while pulling small shrubbery stumps on a landscaping job. The taproot on one stump came loose all at once, and strap slingshot the stump and rootball off the back window of the truck. Straps are also particularly vulnerable to abrasion. In the event of breakage, straps are a lot lighter and softer than either of the other options, and less likely to cause damage or injury.
For whatever it's worth...