The effect of barrel length, and the need for more, is really determined by the cartridge you're firing. The bigger the case for a given bore diameter, the greater the benefit of more barrel length. This is why magnums generally have more barrel length than standard length cartridges, and why short action cartridges often have even shorter barrels. The velocity difference is different between rifles, but generally, the bigger the case, the greater the velocity per inch of barrel. Magnums, and certain overbore non-mags (the 25-06 Rem, for example), really need 24" bbls minimum to take advantage of their ability to burn large amounts of slow powder, and 26" is better. Anything less than 26" on a modern super-mag (Rem Ultra Mags, 378 Wby based cases, 338 Lapua, among others), and you're just wasting powder. Most standard and short action cartridges are fine with 22" bbls, with some taking advantage of 24" (like the 243 Win). IMO, 20" is about the practical minimum for most CF rifle cartridges unless the advantage of a shorter bbl significantly outweighs the performance lost (the M4/CAR-15 for close quarters combat, for instance).

As for accuracy, more than likely a SHORTER barrel will be more accurate simply because it will be more rigid (if the contour is the same). What's easier to flex, a 12" piece of steel 1/2" rebar or a 12' piece? The longer piece will sag noticeably under it's own weight, where the short piece will not. The same is true for a barrel. When the barrel vibrates on firing, the longer barrel (all else equal) will vibrate with greater amplitude than the shorter barrel, making the possible shot dispersion from an "out-of-tune" load greater. Make the barrel shorter and it'll be stiffer and groups will TEND to be smaller overall. Long, thin barrels tend to be the least accurate. To stiffen a long barrel, the contour needs to be thicker, at the cost of added weight.

Mike