That depends on what you mean by "constructed". The individual stages of all rockets are constructed horizontally. The difference is in how the stages and paylo

That depends on what you mean by "constructed". The individual stages of all rockets are constructed horizontally. The difference is in how the stages and payload are integrated. With a rocket like the Atlas V, the upper stage and payload are integrated with the first stage while it is vertical. This is a common approach taken with rockets that frequently fly satellites with big mirrors in them (if the payload is never tipped on its side, it's a lot easier to secure the heavy optics inside). SpaceX does not currently support vertical integration, they only support horizontal integration. Generally speaking customers prefer vertical integration, since it makes their payload design easier (and in some cases it's a hard requirement), so SpaceX will be adding vertical integration support at their LC-39A launch pad (mostly for government launches).