I had the option of branding my Hanoverian gelding when I bought him as a yearling. I chose not to due to the aesthetic reason Bent Hickory mentioned as well as hearing some horror stories, especially about yearlings vs. weanlings. Europe is moving away from branding too.
In retrospect I wish I had, just in case he falls on hard times somewhere down the line and the brand helps him find his way out. He is papered, registered, and microchipped too though so hopefully that would help. But he is a very very plain bay with just a small star, so a brand really would have helped make him at least a bit more identifiable.
I doubt a brand would add resale value to a horse that is already papered and registered, but I could be wrong.
My much older horse has a brand that is only visible at certain times of year in certain lighting conditions. Most of the time I forget he even has it. So you could end up with one of those and all the trouble would be for naught anyway!