Picking nits. If the neighbor paid last time, looks like it is your turn. I would pay, though, to keep my neighbor's DIY hack jobs out of sight. You have a homeowner's association? Do they maintain common elements?
One other way of doing it might be to hire a fence contractor, have them bid it such that it states the portions each is responsible for, and stating materials, finish, colors, etc. Shouldn't be a big deal, and lots of people don't like cracked, patched fences. If you have different tastes, each chooses two colors and styles, put them in a hat, and have the contractor draw one.