Even if in single threaded applications you will increased performance (not just from the extra frequency) as there are 4 cores to take some processes. If the background work load is covered by 2 then the other 2 are free to work on whatever program you are using. So yes, this is a noticeable difference.
Depends on if the programs you use can take advantage of more than 2 cores. Assuming both Core 2 Duo and Quad both have the same clockspeed, the difference in performance for programs capable of using only 2 cores will be very small since background processes generally do not use much processing cycles.
If you use programs / play games that can make use of more than 2 cores, then you can see a decent improvement in performance; roughly 30% - 40% improvement under the best circumstances depending on how well the program / game has been designed to take advantage of more than 2 cores.
Since the Core 2 Quad is 2.66GHz compared to your current Core 2 Duo at 2.0GHz, any program you run will get a performance increase just based on clockspeed alone.
I prefer a quad core over a duo core since that means I can play games and encode video at the same time. Both are pretty CPU intensive so each of those processes will get to use 2 cores.