From litigation I was involved in many years ago, when a strap broke and a steel yacht/sailboat fell injuring a person onboard and damaging the yacht,I know the straps on travel-lifts are special products with identified SWL(safe working load). They should not be repaired by anyone but the manufacturer. Incorrect use or attachment can significantly reduce the SWL. The straps are strong if used correctly, checked for condition,and correctly maintained. The problem is whether slip operators do it correctly.
I also know of boats being dropped off cradles on rails. IMO one is no safer than the other. You depend on the competence of the operator,and, again IMO,some of them are cowboys, working by trial and error, while others are competent and careful. The trick is knowing who is good,and who is not, I don`t think it is a question of which system you use. Though you can usually get at more boat to antifoul if the boat is on a cradle put there by a travel-lift, than on a rail cradle.
I`ve seen a wooden IG50, huge volume boat, (built of meranti!) lifted by crane onto a hardstand supported by props after failure to slip on a rail cradle(stabilisers got in the way). The same yard routinely lifts float-planes onto hardstand for maintenance.
BruceK