If I were to put up a monoband 10 meter antenna would it be better horizontal or vertical? My mobile will be vertical.
I'd go vertical - probably.
Obviously, a mobile antenna would be vertical. It might make working direct path a bit more difficult with horizontally-polarized stations, but that's a decision only you can make.
For DX (not just a couple counties away), vertical and don't look back.
I'm curious why you would suggest the antenna (complete assumption that he IS talking about a yagi) be mounted vertically for DX.
Don't you lose some gain right off the bat with a vertically mounted yagi and won't the mast/tower interfere with the pattern of the antenna? You'll have 8 feet or so of element running alongside. Then there's the issues of more noise with a vertically polarized antenna, take off angle and wind loading.
I would probably mount is vertically only if I were going to use it locally base to mobile or to chat with the locals on 10. Even then probably not with anything more than 3 elements.