My horse is both branded and microchipped
Both were done before I bought him.
The microchip is because the registry required it. The brand is because the breeder does it to all his horses. Given the choice of one or the other, I like microchips better, as it's much easier to match the microchip number to the owner's data than with a brand. I know that the breeder I got my horse from has one of his half brothers that looks almost exactly the same (both are cremello from the same sire) and has the same brand in the same location. If my horse ever got lost/stolen, the brand would trace back to the breeder who may or may not be able to determine if the horse was my horse or one of the other look-alikes that he's bred in the past just by looking at him. With a microchip, he gets traced back to the registry, which has my current contact information on file.