DDR3 generally has a higher clock speed than DDR2, but that doesn't necessarily make it faster. The speed of the memory is a combination of the clock speed and the timings. It's quite possible to a DDR2 module with a slower clock but tighter timings end up being faster than a DDR3 module with a faster clock but longer timings.
The two types are not interchangeable, you have to get the right type for your motherboard or it won't fit. If you're trying to choose a motherboard, go with DDR3 if all the other factors are equal - it's the newer standard and memory for it will be more easily available in the future.