There are a few very good answers on here already, however, I feel that a few pointers have been overlooked.
I am not sure whether 29-ers suit all riders. Height comes into it, a 29-er imposes a high handlebar and heavier wheels than a 26" MTB. IMHO you need to be 6" or taller for the big wheel to make sense.
The distance between you and the top tube is important on a MTB, regardless of your skill level. Most MTB's have a 'compact geometry' with big seat-post. Out the saddle it is useful to not have a 'five bar gate' between your legs, so, if you do go for the MTB, err on the smaller rather than the larger frame. You don't get this with CX bikes as a rule, although I would not be surprised if Giant do make one.
Most 29-ers (if not all) come with disc brakes. CX bikes can come with discs but that is the exception rather than the rule. Disc brakes give much better stopping power, with little need for the rims to clean first. This gives you much better control.
Cyclo-cross pre-dates MTB-ing by some decades and the bikes for the sport evolved from road bikes. Meanwhile, the MTB evolved from a few Californians wanting to have fun, any notion of competition came along later. They were not tied down by UCI rules and UCI rules have always served to hinder rather than advance bicycle design. CX bikes are essentially a legacy product, for a 'formula' sport, not 'pure evolution'. They were not that popular before the mountain biking boom and have not been subsequently. Meanwhile, the separately evolved MTB is the 'weapon of choice' for many, many cyclists and CX ideas such as drop bars have not lasted long on MTB's (they have been tried by Johnny Tomac and Specialized did make a 'Rock-Combo' model with them, this was short lived). Wisdom of the crowds is that the MTB rocks off-road.
For a long time I thought Suspension was a solution looking for a problem. However, there is suspension and there is suspension. A full suspension top end bike by the likes of Cannondale is amazing off road, you can roll over anything without losing speed or control. Cheap suspension is no good at all, i.e. the effort you get on a £300 MTB, perhaps useful for going up a kerb but that is about it. Modern, expensive full-suspension bikes are ridiculously light for how much is going on and a delight to ride. Well worth the investment, unless you are going XC with a bit of road to get to the trail in which case a hard-tail with front lockout is better for the ride as a whole.
If you are a road-bike person then you probably carry nothing. Sometimes it is useful to have a bike you can carry stuff with. An MTB is really well suited to putting a rack on the back and carrying stuff. That may be just a trip to the shops or a long distance tour. Whatever your choice - CX or MTB, do look for those magical eyelets on the rear dropout for putting a rack on there. It may not be what you want to do now, but down the line it just might well be.