I think this question is right up there with "what is the meaning of life", as it's come up for just about everyone I know who rides (as well as myself) at one time or another.
I think it depends on 1) personal preference, and 2) the type of course you race on. Also, the type of full suspension bike can be dependent on the course type too - some are better for downhill and others for XC.
I've ridden about a dozen different full suspension bikes, and my personal preference is the multi-link variety, with something called a "horst link". This is where there's a pivot near the rear drop-out, but the pivot has to be on the chainstay, and it should be lower than the rear axle. This puts the rear wheel on the seatstay section, not the chainstay section.
I like this design the best because it seems (to me at least) to cause the least about of pedaling-induced suspension action of any of the other types I've ridden. I *hate* unified rear triangle bikes, and I'm luke-warm about swingarm bikes (where there's one big link, and the whole rear triangle moves as a unit).
For me I've decided that for now, the extra weight isn't worth it, mainly because of my riding style and the terrain I ride on. Also, my mountain bike weighs in at < 23 lbs, so a full suspension bike would be a pretty noticable weight penalty.
So my advice is to see if the type of full suspension bike you have suits itself to the terrain you're racing on. If not, you might be better off on the hard tail.