Wire rope pros: Cheaper, better at abrasion resistance, not affected by UV.
Cons: heavier, can rust, more dangerous if it breaks, handling more difficult, wire "fish hooks".
Synthetic rope Pros: Lighter weight, easier handling, stores less energy so safer, no rust!
Cons: More expensive, abrades easily against rocks etc. so requires protection, UV degrades.
There are a number of sources for UHMW-PE fiber rope, trade names are Dyneema, Spectra, etc, but much of the offerings on Amazon etc. are doubtless unbranded from China.