Vertical integration tends to be favored with large solids in particular, especially segmented solids like the Titan and Shuttle used. Horizontal stacking and assembly of large solids is tricky--note that every rocket to use them has been vertically assembled: Titan III and IV, Shuttle (both in the existing VAB at Canaveral and in the alternate setup at Vandenberg SLC-6), Ariane 5, the Atlas and Deltas. The Russians have always steered away from solids, and thus the horizontal assembly doesn't have the issues for them.
The advantage of horizontal assembly is that during assembly, the entire vehicle is the same height off the ground--a single set of platforms (or even just ladders) can access the entire vehicle. However, unless there are also vertical access systems at the pad, you have to tip the rocket back down to work on it--and if there are vertical access systems, the rocket is now being serviced in two orientations, which effects the human factors of the handling process. If a vehicle is processed vertically, then you do need more platforms and such, but once built there's not a tremendous difference in operations cost, and the completed vehicle only needs to be maintained in the vertical position, whether at the pad or the assembly building. Also, thanks to years of legagy, many western payloads are designed for vertical processing themselves, not designed for being held cantilevered on the front of an LV but instead supported through their long axis throughout integration and rollout and thus the rocket must still be tipped vertically for final payload processing. This is actually something SpaceX is having to deal with in their attempts to setup for bidding on DoD payloads IOTL, as I understand things.
On the whole, I'd give a slight advantage to horizontal integration, both in initial infrastructure requirements and operational benefits (at least for a traditional multi-stage tube rocket), but the presence of large solids can tip the balance in favor of vertical integration, as can existing infrastructure and traditions, and the resulting effects on the payloads being designed. If the Russians made more use of solid boosters in their program and the Americans less, you might easily see the situation reversed.
And Shevek, I'll note that I specifically addressed your points about rollout in that same thread
here. If you have an issue with myself, or truth is life, I'd appreciate that you bring it up there or in a PM, rather than bringing it up passive aggressively in another thread months after the fact.