I'll add a few observations I haven't noticed in the above posts: Please use your own brain to evaluate them, there is always a chance that I am full of %#@t.
There is a learning curve when switching from steel to synthetic.
Care and use
(1) Steel is easier to spool smoothly onto a drum, but much less forgiving when you do it wrong. A steel cable that's wound incorrectly can form a "birdcage" that will affect the strength of the cable. A synthetic cable that is wound incorrectly is much less likely to damage the cable, but its also requires more care to wind correctly. The "softness" of the synthetic cable is not as good at pushing the line laterally as it spools onto the drum. This makes it more likely that the synthetic will wrap across itself. Synthetic is also more likely to wedge itself down into the gaps in the layers beneath the one being wound. This results in the cable being pinched and makes it difficult to free spool the cable.
(2) You need more tension on the synthetic cable to properly install it and wind it in. (see the "gaps" comment in note 1).
(3) We do a lot of scrambling up and down tall steep dunes here in Dubai. The synthetic cables are sooooooo much easier to work with when you have to climb up the dune to your anchor.
Ease of Handling
(4) Synthetic is also much easier on the hands. I know we are all manly men who don't care about such things, but my wife uses the gear as much as I do.
(5) I think the UV issue with synthetics may not be as big an issue as it once was. I know manufacturers have been working on the issue, and I have no science to back this up, but I am not seeing any difference in lifespan between the ones out here with covers and the ones exposed to daily sun. There are a lot of old synthetic cables out here, and nobody breaks them. Even the scary looking fuzzy ones. (note that the sand recoveries we do here do not put nearly as much strain on the cables as mud or rocks.)
Safety
(6) I also think the safety factor is a little overblown. Not because synthetic isn't truly safer, but because, in the applications we generally see, steel cable is not really as dangerous as its made out to be. It can hurt you, but I don't think its as bad as its reputation.
The danger from "snap back" comes from the stored energy in the line. The amount of stored energy is the product of two things: (1) the amount of stretch in the line; and (2) the weight of the line (or attached projectile (think tow hooks)). Both synthetic and steel cable score very well in the first category. Synthetic stretches less, but steel hardly stretches at all in the lengths we use for a recovery so there isn't much real gain. The internet tells me that steel cable stretches about 0.1% (most broken-in cables will stretch less), so the 50 feet of cable you usually have out will only recoil about 0.5 inches. Shorter lengths of cable unwound will recoil proportionately less. Synthetic is much better in the weight category, but neither is really a huge threat unless there's a projectile like a hook, shackle or tow point.
I have seen a steel cable part on a 12k winch. It dropped to the ground and coiled up like a slinky. The guy had about 80 feet of line out and the cable parted about six inches from the hook. The frayed end of the cable came to rest about 10-15 feet away exactly in line with the pull. Most of that distance was the result of the cable gong back to the coiled "set" it had taken from being stored on the drum. If you had been straddling the line when it broke it would have scared the crap out of you, but it would not have torn your blue jeans. Much less killed everyone in an 80-foot radius like a giant guillotine. A whipping cable on a 4wd recovery can scratch paint or put your eye out, or cut you, and should be given due respect. But its not nearly as risky as a snatch strap. I am not advocating that you be stupid or take chances you don't have to. Be safe, follow all the best practices, but don't be scared of the bogey man. I think you are actually in much more danger if the cable holds and the recovery point breaks. That 0.96 inches of acceleration might put a lump on your head if there's a shackle attached.
Snatch straps on the other hand are extremely dangerous if mishandled. They store infinitely more energy (advertised 30% stretch instead of 0.1% stretch), and are usually much stronger than the tow points they are attached to. The shackle on the winch cable will leave a good bruise, but the 20,000mph tow hook on the end of an unbroken snatch strap will go through you and the car behind you.
Durability
When we all had steel cables everybody knew-somebody-who-knew-somebody-who-heard-about-a-guy that had seen one break. Now that synthetic cables are popular, lots more people seem to have actually gotten to experience it first hand. I don't know if that means anything or not, but it's food for thought.
I love my synthetic cables in the desert where there are no rocks or trees that will abrade the cable. They last a good long time out here. But back in southeastern U.S., I wouldn't want one. My recoveries there always seemed to be in places that often involved rocks or ledges or trees or some other obstacle or tourist in the way. The cables took a lot more abuse there. Back home, I still have a 20-year old cable on a Warn 8,000 lb winch that remains in great shape after a lot of use and abuse. I don't think a synthetic line would still be there.
My concern on durability is not the expense, but rather the consequences of it not doing the job when you need it. After using both types for a number of years, I think that in most environments, a well maintained steel cable is less likely to fail when you need it.