A strop has No or very little give its made for lifting or winching it can be used when towing if you take up the slack and then drive once the strop is taught. This will work if a vehicle is semi stuck and needs a little helping hand. The same thing is true of a wire rope or even towing chains. Nobody here would suggest you go and buy either of these to be used for recovery but many advise you buy a strop. Why I do not know, lack of knowledge maybe. A rope will work as above (except winching) you can get rope taught and drive off for when the vehicle stuck needs a little help.
A strop is cheap. its light it needs little maintainance and handy! I have plenty. What they are terrible at and what alot of people do with them is try to recover more stuck motors with a little run up. This puts 100's of tonnes instant force on all towing points, shackels, drivers passengers backs instantly. It usually results in ripped off towing points (Even rated ones) bad backs and stupid forces instantly usually ripping the sticting in the eyes out of the cheap strops.
There is always an exception...........Procomp do a semi kenetic strop which is good but my money is on a good old fashioned nylon rope like these:
TRADLINE ROPE & FENDERS - 4x4, OFF ROAD & RECOVERY
(first link I came to)
I have had one of these and it has been abused and abused many many times in 10 years. I did buy a new one as it was lent to somone and it came back damaged as they only had cheap strops. Lesson learnt!
This rope you can use the weight of the towing motor to help get things that are really stuck moving Simple! also as before take up the strain and drive off. it has some give and will not put instant forces on your backs nor the vehicles recovery points nor equipment.
Lots of recovery people use strops but they usually use large winches on trucks and or recover things as described take up slack and drive off. This is sometimes not practical when something is really really stuck. Where a strop will take many back jarr ing pulls a single pull with a rope can be way more effective.
Take for example team recovery a race to complete 3 impossible hill climbs 2 motors using only rated ropes.
ALRC National trials 2011 Team Recovery - YouTube
I forget how many times people turn up at the offroad club with their rated strop to be laughed at by the scruteneer. Strop for winching or gentle tug. Rope for recovery Simples.