For diving position between vertical or horizontal [ also called prone for diving, meaning face down in the water] there are a number of studies regarding work and breathing efficiency. Its summarized in Bennett & Elliott's ... Diving Medicine.
In a nutshell, some studies show it is easier to breathe in the prone position, and in some studies no differences were found. For heavy work, position shows no difference, but its far easier to work in the vertical position. Navy and commercial divers do not use fins work vertically, often with weighted shoes.
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=Abstract&list_uids=11820330&query_hl=1&itool=pubmed_docsum
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=Abstract&list_uids=1561722&query_hl=1&itool=pubmed_docsum
In over 1000+ dives I've done, I find it hardest to breathe in the upright or vertical position the shallower you are and supine, that is face up in the water. These findings are all supported by many studies on OC scuba, it has to do with compression of lung volume and the cracking pressure of the regulator.
Usually past 30' and far deeper, the only advantage true prone position has is in swimming efficiency especially against a current, it provides the smallest surface area to current.
I have witness several accidents, with no major consequences, by the rigid teaching of this prone position, often to new divers. The prone position is not optimal to obtain leverage to remove stuck hoses quickly especially in cold water and gloved hands; gas bubbles in a wing are only maximally position for venting when the vent port is vertical ... best on top of the wing towards the inflator hose. In there is a runaway power inflator, the vertical position allows venting even before the wing fills. In many wings, the bottom segments are slightly wider and are not joined into a continuous loop, so venting the rear port exhausts only half the wing. A leaking LP hose can be snapped off in 1-2 seconds, versus the number of turns needed to shut a valve on the offending post.