This question comes up all the time, there should really be a FAQ for it. I'm bored today, so here's my attempt:

-What's more powerful, V-brakes or discs?
The answer is either A)neither, or B)it's irrelevant. Properly set up discs and v's will both lock the wheel with one finger on any terrain, save perhaps rubber wrestling mats or something. Yes, you could put a 12" motorcyle brake on your mountain bike and it would lock the wheel with even less effort, but beyond a certain point, this is useless. Mountain bike brakes reached the point where power is irrelevant with the advent of the v-brake.

-Ok, what modulates better then, smart guy?
The answer is the same as to question 1. Assuming everything is correctly set up, a skilled user can modulate either type of brake well. Modulation, in fact, is so good that locking a wheel unintentionally on the trail is probably rider error 99.9% of the time. There are bench tests that show better modulation characteristics for discs, but you would be hard pressed to feel these in any but wet conditions.

-Aha! So discs are better in the wet?
Yes. If you ride in wet conditions, disc brakes are undeniably better. This is the consensus of 95% of all mountain bikers, with the other 5% being retro grouches still hanging onto their Onza cantilevers for dear life.

-Wait. I thought you were one of those people who hates disc brakes...
I ride discs on some of my bikes and v brakes on others. Your choice in the matter is subjective and highly personal. Trying to convince someone else that your setup is better is a waste of your time. Go riding with them instead - you'll probably find that their skill and fitness count for a lot more than their bike setup.

-Ok, I'm a total goober who is only capable of purchasing things recommended by the wise ones of MTBR. Should I get discs or v's?
You need to ask yourself some hard questions here:

Question 1: How much money do I have?
A good solid set of V-brakes can be purchased for around $20. Don't believe me? I'll sell you a set to prove it. A good solid set of discs can be purchased for around $120 (this is the best price I've seen for a set of Avid mechanicals, which IMO are the cheapest decent brake out there). You can of course move up the scale of quality, and that $100 price differential will pretty much follow along. If you think $100 worth of beer, or tires, or not working at Taco Bell for 14 hours is worth more to you than disc brakes, then you should get V's. Remember that you may have to get different wheels if you're changing your current bike (for argument's sake, I'm assuming you're building a new bike from scratch).

Question 2: How much do I ride in snow/ice/mud/rain?
If you live in Colorado, Texas, Utah, New Mexico, Arizona, or parts of California, you probably will seldom or never need the wet weather advantages of discs. If you dislike these types of conditions anyway, then you probably also might as well get v's, since you can get yourself some beer with your extra money in the event that it does rain and your ride is ruined.

Question 3: How much does weight matter to me?
All other things being equal (meaning you're going to invest the same amount of money either way) you'll save some weight with v's. How much? That's a matter of how well you shop around, and how well you "tune" (ie add aftermarket hardware and/or modify) your brakes. Call it 3/4 of a pound to keep things simple. This isn't a lot of weight, considering that you+your bike are probably between 170 and 200 pounds, if you're reasonably fit and already have a light bike. But it IS weight, and you WILL go faster without that weight. Of course, if it starts raining in the middle of your race, you might also go a lot slower because of that 3/4 of a pound.

Question 4: Can I true a wheel?
If not, you're in big trouble regardless of what brakes you get, but you'll be happier with discs, because until the tire hits the frame, you can keep riding along and your brakes will work well. It might be better at this point to invest some money in tools and a repair book instead of OR in addition to your disc brakes, though.

Question 5: Can I bleed a hydraulic line?
Disc brakes are a bit more complicated than V's, and if you don't know how to do the work yourself, you might end up spending a lot more money at the shop getting tuneups. Shops will charge you more to work on discs, in general. For a small investment of around $10 at the hardware store, you can be set up to bleed your brakes - it's worth learning how to do. If course, if you have mechanical brakes, this is irrelevant.

Question 6: Am I going to put discs on a singlespeed?
If so, think carefully about your decision. In order to keep the pads and rotor lined up, you're going to have to do some drastic things to your bike. You can get a bike with an eccentric bottom bracket (Phil Wood makes most of these, they're real works of art), which is a pretty-looking but heavy and complicated innovation which allows you to tension the chain from the crank end. Alternately, you can accept having to move the disc caliper around to line it up every time you re-tension the chain. If you're using a singulator or other chain tensioning device, these points are moot.

-Can't you shut up?
That's the beauty of the internet. A scrawny 15 year old girl could be writing this, and you'd still have to sit there and take it. But yes, I'm about done. Brake decisions are not life and death (except perhaps if one decided simply to forgo them altogether!), just pick something that you think will work well for YOUR financial constraints, riding style, and location. Both have advantages, both have disadvantages, but neither is going to make you a better rider. Only practice and dedication can do that.