Horizontal nests are better for almost all applications, in my opinion. This is why most of the product lineup at arthropodantics.com are horizontal nests. That said, vertical nests do have a few specific advantages, largely being able to house more ants in a smaller surface area (due to being able to stack upwards, rather than expand outwards for more nesting space) and for species that have repletes, such as Myrmecocystus, or otherwise have a knack for hanging upside down in the nest.
With horizonal nests, the main advantage is visibility. With almost any example on the market, a horizontal formicarium is going to allow you to see your ants the best, especially if it's a nest with shallower chambers (or none at all). Even with Arthropod Antics' vertical Formicaria, where visibility is a huge priority, they are still outclassed in that aspect by the horizontal formicaria in our lineup.
If you're just getting into the hobby, and with the species you have mentioned, I would strongly suggest a horizontal formicarium. You won't need to worry about space, since with only a few colonies you should have plenty of desk space to accommodate a couple of setups, and having a setup with excellent visibility will certainly encourage you to watch your ants, and just further grow your interest in antkeeping as a whole. On top of that, Camponotus species have no need to hang upside-down in a nest, so verticality is not something required in a captive setup for them.
