The advantage of the dual-core processor is that in some applications, ie: those that are designed to take advantage of it, having two cores can significantly boost performance. For single-threaded apps like games, there's not much difference. You can also expect Windows as a whole to run a bit faster on a dual-core, since the application workload can be distributed amongst the cores. Don't expect a huge increase in performance, though.
The disadvantage of dual-core, of course, is that it can be more expensive. If the price and clock speed are the same, I'd go for the dual-core, naturally.
In the case you propose, it's really hard to choose. The 2.0Ghz Turion might be faster than the 1.6Ghz Turion X2 in single-threaded applications.
What's the price difference between the two? What is the computer intended for?
SuperPi 1M: 29.6s - 3DMark06: 8616
The Geek Test v3.1 Score: 36.3% - Major Geek