Both are dual core, 64 bit cabable processors. Which is quicker very much depends on what specific model you are talking about and the bus speed/memory configuration.
Core 2 is typically faster, but uses more battery than a Turion will. The Turion 64 X2s are pretty good price wise and battery efficient. Core 2 duo is a big improvement on the Core 2 but is more costly.
The better the bus speed of the motherboard , the better performance you are going to get between your processor and memory, and that is what counts.