Bye-bye finger squeak!
I like both the Nano- and Poly-coated Elixir strings, but the thing I particularly like about the Polyweb strings is the reduced finger noise when you slide your fingers up and down the strings. Apparently the thicker coating fills in some of the space between windings on the wound strings, and this greatly reduces annoying finger squeak. Some people have the opinion that this coating reduces the brightness of the strings. Although I have not done a comparison of both types of new strings on identical instruments, to me, these strings sound fantastic. I've tried both types, and I think the Polyweb strings sound wonderful, and the reduced finger noise is the reason I prefer them.
I use only Elixir strings because they sound great and keep sounding great many times longer than other strings I've used. I play acoustic guitar about 5 hours a week, and I use a set of strings for about 3 months before changing them. After 3 months, they still sound good, but a new set sounds better. Concerned about the price? I get over 60 hours of playing from a set, so the cost per hour is trivial. I know some people use them much longer than I do. I used one set for a year, and I still thought the guitar (a great guitar, by the way) sounded good. Changing them every 3 months feels like a luxury I can happily afford.
People tend to hear what they expect to hear. I suggest trying these strings with an open mind. I think you'll like the way they sound very much.