mountain bike vs. cyclocross bike
Cross bikes are generally ok for less serious trails where you're looking for decent speed, without the need for serious climbing, suspension and traction. 

You've got more clearance on a cross than a road bike, but the frame is a similar size and they've generally got 700mm road size rims, so they aren't as maneuverable as an MTB. They generally don't have suspension. Tyres are fatter and with more tread than a road bike, but they'll normally only get to about 32-35mm width - MTBs will go wider. The gear ranges reflect this too - you'll be able to go faster at the top end, but the lower end gears to tackle the serious inclines will be more favourable on MTBs. 

In general use cross bikes are great for road use with a bit of off road, where MTBs would be the other way around - especially if you're going to be going seriously off-road.  

The 'real cyclist' answer is to get both. After all, you'll always need another bike, right?