Those old English warbows were the answer to a question that is not frequently asked by archers and bow hunters today. Those bows were meant to launch very heavy arrows into the ranks of the enemy. Certainly accuracy was important, but probably not as important as it is to a modern day tournament archer or hunter. Contests of those days were shot at longish distances to hone the skill of placing that arrow into the ranks of the enemy.
Today we lump many designs as "longbows". Bows of 66 to 72 inches provide a steady platform for many archers, but not all! There are individual shooters who excel with these longer bows and others who find a shorter R/D or recurve to be more to their liking.
I've always been of the opinion that individual skill is more defining of accuracy than the style of bow. When a shooter exclaims that his new bow stacks arrow after arrow into a tiny little group, he/she is selling his/her skills short. What has happened is the shooter has picked up a bow that is a good fit to the shooters skills.