No one has mentioned it here, but one of the big advantages of a longbow is the lesser chance of limb twisting. It makes stringing and unstringing without a stringer possible too. A related advantage is the strength of the limbs which are thicker from the back to belly and not as wide as the recurve limbs, so they are generally tougher and not as easily damaged. As has been said by other people here, carrying a light little longbow all day long, especially in hilly or mountainous terrain, is much nicer than hauling around a bow that weighs twice as much or more. But those light, little longbows are not as stable and therefore not as easy to consistently shoot accurately. Howard Hill made that observation when recommending longer longbows over the shorter ones. New designs, like the Shrews, have helped in that area, but weight and length will always have an effect on stability and accuracy. Every mechanical design is an exercise in tradeoffs and compromise.
I like both styles about equally, particularly when we are talking about reflex/deflex longbow limbs versus recurve limbs. There are also working recurve limbs and static or semi-static recurve limbs. There is as much variation in recurve limb design as there is in longbow limb design. I have about 40 bows and shoot various ones regularly. Depending on the individual bow and its characteristics, either a longbow or a recurve can shoot just as accurately at any distance and can be just as quiet. Going from one bow to another is not a big deal, but it does take a bit of adjustment in my shooting. There is no doubt that shooting the same bow all the time would produce greater consistency, but I like variety. There is a saying in firearm shooting to, "Beware of the man with only one gun", because he gets so familiar with it that he shoots it very well. The same expression could be used for the archer with only one bow.
Allan