Lots of different answers and possible solutions, and it's not all about which tyres, although If you have confidence in them that's half the battle. First, are you over thinking the problem? If you think you may slip or lose a bit of grip, then you'll tense up which will make matters worse. Try and relax. Rear wheel slides are not the end of the world as long as you can ride them out, and they may actually add to your cornering if you can control,them. Front end drift is another matter, and has different consequences. Try to keep your weight neutral over the bike when cornering, whether up or downhill. Your weight should be going vertically down through the bottom bracket, which means you need to weight shift to achieve this, shifting your body mass forwards when climbing, but not so far as to lose rear end traction, and slightly backwards downhill, but not so far as to unweight the front wheel.
On rough stuff, your tyre pressures and suspension need to work together to keep the wheels in contact with the surface. Adjust your fork if you can to absorb hits without bouncing back off the surface, and lower your tyre pressures so that your tyres themselves can mould themselves to the trail rather than skipping about.
Control your speed. If you go into loose stuff, especially downhill, too fast, any braking will make the wheels lock up. Brake before loose turns and let the bike find its own way through. It doesn't want to fall over any more than you do, so choose places where you can scrub off speed in a straight line, then let the bike run, looking for the next chance to brake
Practice, practice, practise.