Well no actual experience with boats here, just winches and hoists in general.
Straps are more likely to break then a cable, but they are easier to use and you won't get a problem with it not laying onto the drum correctly like cables can sometimes
Cable is far stronger and less likely to snap under load, but it's not as easy to handle and work with as straps and if it frays then you run the risk of getting strands of steel cable embedded in your hand (that hurts, but to be fair, if it's frayed you shouldn't be using it). Also with a cable you have the option of attaching a pulley block to the item your trying to pull/lift and running the cable through it and back to the winch and therefore doubling the winch power.
I personally would go for straps for the ease of use, but make sure the strap is rated far in excess of the weight you will be lifting with it.