Braided polyester rope is more abrasion resistant and stretches less than comparable nylon lines.
It holds up better than nylon when exposed to sunlight, and is almost as strong. And it has better dielectric properties (is less likely to conduct current) than nylon.
On the other hand, it does not absorb shock loads as well as nylon and its dielectric properties are not as good as those of polypropylene.
12 strand diamond braid and double braided polyester are used by tree care, roofing, window washing, and rigging contractors as vertical lifelines in fall protection systems, and by tower builders as guy lines.
Tree care contractors use double braid polyester as bull rope, climbing rope, and positioning lanyards. And they use it with a steel cable in the core in fliplines (the steel core style is not used when working near power lines).
Electrical and outside plant contractors also use double braid and 12 strand constructions as cable pulling ropes.
Pulling tapes (the polyester yarn is converted by weaving vs braiding) are used here as well.
Solid braid polyester is used flagpole halyard, and as transmission rope in automatic swimming pool covers, sometimes with a core to minimize stretch.
Road building contractors use 1/8" diamond braid polyester with low-stretch dacron or kevlar cores with curb and gutter machinery that uses sensor cord (string line).