If you do not mind a trellis, I would build a tall arbor, to ensure that even in the winter, you view is not their camper, and I would plant grapes. It may take a few years to grow up and fill in, but the sweet rewards are twofold- no ugly view, shady spot to relax under and eat the fruits of your effort.
Another idea, if you want winter color is Arborvitea... I personally do not like them, to me they are just breeding grounds for spiders and snow can make them misshaped if you do not wrap them.... and wrapping is ugly too.

Atleast the grape vines and arbor will make for an interesting winterscape.
As far as the neighbors... if a grapevine goes astray and onto their side of the fence, well, let them cut the vine... it will not hurt the plant in the least.

You can also hang windchimes from your arbor. Add a little bench under their and you have created a little oasis from the world.

I have the same problem. My neighbor has a split rail fence along half the side of our yard and they have a horse trailer and old fishing boat and old wood and it looks messy. I wanted something evergreen so I went with the Emerald Green Aborvitae but only have it half way done but it looks really nice. I thought about grapes or wisteria which would be beautiful but went with the evergreen.

Consider bamboo. You will have to trench and install a root barrier for the cold hardy runner varieties, but it can provide a relatively quick & nice looking privacy screen.