4WD = Low range and High Range gearing
AWD = Only high range gearing
Part-time 4WD: No centre differential. Cannot be used on dry/wet, semi-slippery roads due to the lack of the centre differential. When activated, both front and rear axles are physically locked to each other and have to spin at the same rate. This becomes a problem when turning on sufficiently high friction surfaces. Examples: Suzuki SUVs, most 4WD pickup trucks, cheaper SUVs.
Permanent 4WD:. No two wheel drive mode. System is equipped with a centre differential, and hence is safe to use on all surfaces. All four wheels are powered all of the time (usually 50/50 front and rear axles). This is arguably the best system since the torque split ratio does not change and is the most predictable. All wheels "help out" all of the time and this stabilises the vehicle + improves handling. With the extra two drive wheels, the vehicle has twice the amount of traction all of the time (even in no-slip conditions) vs. a 2WD vehicle. Examples: MB M-class SUV, the Range/Land Rovers.
Full-time 4WD: Basically permanent 4WD but with a 2WD mode. This was born out of customer demand (for a 2WD mode). Examples: Toyota Sequoia, Mitsubishi Montero.
Permanent AWD: Basically permanent 4WD but without low range gearing. Examples include the Audi Quattro AWD system, the MB's 4-matic AWD system, Subaru's manual transmission AWD system.
Full-time AWD: System is active at all times, however in most cases, the one set of wheels (usually the rears) only receive 5-10% of the engine's power unless slippage occurs. At that point, power is progressively transfered to the opposite axle to help out. Some systems can transfer power to the rear upon acceleration to improve traction. However, they revert to 2WD mode when coasting.
And that's not all the nuances, and I really didn't address your question (what's best for you may depend on why you need 4WD or AWD). Check out these CarSpace discussions for more:
4WD & AWD systems explained
Toyota 4WD systems explained