A few years ago I asked this exact question to the archetier who made my bow.
According to him, bow weight and flexibility are the things to have in mind when having a bow built. These are the things that make a difference in a bow.
Now about it being round or octagonal, it was a purely aesthetic decision. The bow can be heavier or lighter, jumpy or stiff, and still be either round or octagonal. This question is in the same league as "should my bow have silver ornaments or some cheaper metal?" and "how detailed should the mother-of-pearl engraving be?". Purely aesthetic.
Sure enough, I called my archetier and he confirmed that it's an aesthetic question. There are factors to have in mind that differ when building the bow, but the way it works is all the same. Mind you this answer comes from a guy who makes bows for a living, whose father made bows for a living before him and etc. Plus half the orchestra I work at uses his bows, so I guess it's a pretty reliable source.