They both have the same meaning. Sometimes in English we add 'up' and 'down' when we talk about moving in a direction. We often say things like "The garage is down the street." We could also say "The garage is up the street." We don't actually know which way is up or down (unless the street is on a hill), this is just common wording of native speakers. If you're traveling a far distance then up and down refer to the directions north and south on a map. "Let's go down to the Bahamas!" or "Let's go up to Canada!"

Both are equally correct. We tend to add 'up to' and 'down to' at random in these cases. You could have said "I had to take it up to the garage, there’s something wrong with the engine!" and it would have been correct. 'up to' and 'down to' have nothing to do with height.