What is the basic difference between horizontal and vertical thermosyphon reboilers other than the vaporising sides.

The main difference is their application: vertical termosyphons are employed for smaller duty services (less % of vaporization), clean and low-viscosity (<0.5cP) process fluids, for stable applications where changes in tower feed flowrate are minimal. The selection also depends on available elevation. There is an obvious cost advantage of vertical over horizontal thermosyphons, but only in the case if vertical exchanger is fully applicable.

Google reboilers, you'll find a lot of interesting stuff.