It's just easier access and more convenient to work on a tall thing that's on its side, rather than having to pick stuff up with cranes to put on top of the tall thing, and require lots of gantries for access.
However for the most efficient structure, i.e. the lightest, you would like to not add load cases for ground handling that are substantially different from flight. Launch vehicles are designed to handle loads predominantly in the longitudinal direction. The orthogonal loads are much smaller (unless you lose attitude control, in which case you see spectacular breakups as large aerodynamic forces are applied in other directions). If you build it up vertically, then the ground handling loads are in the same direction as the flight loads.
If on the other hand you build it horizontally, now there are lots of new load cases for the structure to handle that it doesn't need for flight, where parts of the structure are supported on one side to take the weight of the whole structure. There are even more load cases in the process of erecting the launch vehicle, taking it through all angles between 0° and 90°.
These load cases might not be too bad, since you never load propellant horizontally, only vertically. Far and away most of the mass is in the propellant. Still, you can make a more efficient structure if it is kept vertical from the get go.