Both bows are made for different reasons and different uses, but in general, a longbow is more "forgiving" than a shortbow, therefor considered to be more "accurate"; the accuracy comes primarily from the arrow and the archer's skill, not the bow. (Old Archer's saying: "Any stick can be a bow, but a poorly-made arrow is just another stick.") Both bows are capable of shooting an arrow the same distance, depending on the actual design of the bow and the materials used to make the bow. The main difference between the two types of bow is the longbow provides a smaller angle from arrow to string, when the bowstring is pulled back to full-draw. This greatly reduces the amount of what is called "string pinch", which makes it easier on the fingers of the string-hand, which is the hand used to pull back the bowstring.
It is thought by some that the shortbow was first made to be used from horseback, such as by the mounted warriors of the Mongols and other such Cultures and Peoples; nobody really knows for certain just when the basic shortbow design was first used, though. In general, though, a shortbow is primarily designed for use where a longer bow would be impractical (such as on horseback, where the archer must be able to swing the bow across the horse's head and back - or in dense woodlands, where a longer bow would likely get snagged in tree branches and brush).
Note: Most longbows have a greater nock-to-nock length than a recurve of comparable draw-weight, so simply saying a bow is a "longbow" or "shortbow" just because it is longer or shorter than another bow can be somewhat misleading. It is that acute string-angle at full-draw which truly differentiates the two types.
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The question does not specify what is meant by "Better" Since the two bows are vastly different, you really need to clarify what you mean. If you mean in power, the crossbow wins every time, Medieval war crossbows were so powerful that they had to be "Spanned" (drawn) by a mechanical device, being beyond the strength of a man to draw back. Of course that meant that a longbowman could shoot about a dozen arrows while the crossbowman was reloading. Shooting a crossbow is also much easier, anyone can pick up a crossbow and shoot pretty accurately, not so with the compound, recurve, or longbow, which require a lot of skill and practice to use accurately.