Bar wrapping is an acquired taste. I used to hate it, now it is a labor of love, and adds either the finishing touch, or freshens up a older bike's feel and look. I like Brooks leather wrap, though it is pricey. I found a Chinese product, Kingou, on Ebay for 1/4 the cost of Brooks. Its synthetic, wraps easily, provides just the right amount of "cush", and doesn't seem to darken or stain like the Brooks does. I've always wrapped end to top, mostly because I use bar ends, and don't want to deal with cables and removing the shifters. I've tried Fisik on a couple of modern bikes, like the look, wraps easily, but could use a little more "cush". I like the overlap pointing out, so the edges lay down and don't lift with use,
Brooks leather on '73 Super Course. This is right afrer application. Now, shows patina of sweat stains, hand oils, and 3000 miles, but is holding up well.
'78 Super Course with Kingou synthetic. Nice feel, doesn't seem to stain, and 1/4 cost of real leather. I have it on two bikes, both with honey color Brooks saddles.
Fisik yellow on a modern bike. I spray painted the plastic plugs to match. Like the look, but the tape could use more cush. The top bar bag isn't really that big, just the camera angle.
My Peogeot on the left with the Kingou synthetic, a friend's on the right with tricolor cloth wrap.