Short frames have a distinct climbing advantage. The shorter wheelbase provides better leverage and traction when climbing hills: The steeper the hill, the more advantage. This is due in part to the ability to get your torso forward on the bike while keeping your body weight above the pedals. The compact design of shorter frames also has a geometric advantage: It keeps the drive-train shorter, moving power to the back wheel more directly and efficiently.
Shorter wheelbases handle better. One thing to note, though, is that shorter frames do not mean less clearance. Shorter framed mountain bikes still maintain the same clearance above ground as larger frames. There's plenty of clearance for bouncing over rocks, logs, limbs or any other obstacle. And with the shorter frame, you can turn sharper and you don't need as much room in technical riding situations. And if you get in trouble, you can always jump off, throw the bike on your shoulder and carry it through rough terrain faster than larger frames.
Balance is vital for mountain bikes. Short frames have a narrow center of gravity that will balance more efficiently. Some rugged trails have little or no room for error. The balance factor can be very important when riding across small bridges, along the top of flat rocks or even on specific water crossings built for mountain bikes that have a narrow platform. Large frames can be hard to balance simply because there's much more frame around you.
Weight is another factor considered by cyclists. Weight is so crucial that many cyclists weigh bikes and bike parts in grams. For example, a paper clip weighs about 1 g. When comparing large and small mountain bike frames, the difference can be astronomical when compared in grams. Every cyclist takes weight seriously, and short frames weigh considerably less than large frames. Serious mountain bikers also get into situations that require them to carry the bike on their shoulders. The less the frame weight, the better.
Most people don't realize it, but bike frames flex when you ride them. It's a subtle bend that happens mostly when you are pedaling the bike with force. This happens mainly around the bottom bracket where the axle goes through the bike frame. When you push hard on the pedals, the bike bends in that direction. You might notice this as a slight clicking sound when rounding a corner while pedaling. Large frames bend more than short frames. In time, this can wear out your bearings, your front gearing or both.