I have access to a lot of round stainless steel bar stock and this is what I was planning on using however I see lots of tool makers using square bar stock. Is there any advantage or disadvantage as to which to use?
There
may be.
If you use square stock, then there is a natural position for the tool to take on top of the tool rest - it will ride flat on the top of the tool rest. On the other hand, if you use round stock, there is no natural position, and instead you must consciously choose a position for the tool
Carbide tools are essentially scrapers, and ideally should be pointed slightly downward at or slightly below the centerline of the headstock spindle. That part is easy.
In addition, you have a choice of angle - you can choose a flat (9oclock-3oclock) angle, or a slight tilt for shear scraping (say 8 oclock-2oclock).
For new folks, the safest approach is to have the tool rest slightly above center so the tool angles down, and then tilt a bit to the left for a shear scrape.
If the shank is square, it will naturally orient to flat scraping, and if shear scraping is desired, a slight counterclockwise twist away from that neutral position will get there. But if the shank is round, there is no natural 'neutral' position for the tool, so the user has to think a bit more about tool orientation.
There is one manufacturer of carbide tools in the UK who use square stock, but with a slight twist in the stock toward that shear angle.