As someone who had their face waxed a few times... yeah it hurts. The thicker and coarser the hair the more painful it will be. If you go down this route have it done by a professional waxer that way you know it will be done properly and they will fix up your skin post treatment (bleeding is not uncommon the first time or two).
Pros - cheap, quick, gives a nice smooth result (once any initial swelling, bruising and/or goose flesh goes down... these are usually most notable after the first treatment or two).
Cons - hurts like crazy, especially the mo. Does grow back, and quicker than you'd expect. I was often plucking hairs out within three days - I suspect these were hairs below skin level at the time of waxing. Can lead to ingrown hairs which can cause infections and painful bumps under the skin (I once liberated one ingrown and it was over an inch long). I am told by my electrolysist that waxing can, over time, distort the follicle shaft making electrolysis/laser difficult if not impossible... I have no proof to back that up.
Does it lessen the thickness and coarseness of the hair? Some say no but my experience was that, in combo with E and low T in my system it had some kind of effect on those hairs... less coarse, more sparse and less curly.