Vinyl will also last forever while wood will be lucky to last 20 years.
You can have it “look funny” now and just do the other side later. But I don’t think it would look unusual to not have fences on each side match, especially if there is already different landscaping on each side.
My bigger problem with vinyl is cheap vinyl fences are still a somewhat expensive and look cheap and ugly, while wood-look vinyl is extremely expensive.
