the Q6600 will consume more power, so over time it will cost a little more due to electricity costs.
Single and dual threaded apps will run a little faster on the E8400, multi tasking and running quad enabled tasks will be much much faster on the quad.
generally it is:
E8400: 1-2 cores (depending on task) x 3ghz core speed + 0-50% more efficient (usually around 10-15%), depending on task, because the E8400 is newer generation part compared to Q6600 - inefficiency due to multithreading (task dependent, non existent in some).
Q6600: 1-4 cores (depending on task) x 2.4ghz core speed - inefficiency due to multithreading (task dependent, non existent in some).
However, generally speaking, tasks that tend to benefit a lot from improvements in the new gen will scale very well to 4 cores (aka, video editing) so the quad still wins by a little (or a lot) on those.
In many games the dual wins since they only use or or two cores (2x3ghz for the dual, and 2x2.4ghz on the quad, with the other 2 idling). In others all 4 are used well (rare, but there are some games like that, those games are generally more intensive so they actually NEED that extra power, compared to dual core games that can run comfortably on the quad). In other games neither matters since you will be GPU limited instead.
If you intend to not do video ENCODING (creation, that takes hours, not watching a movie), and you don't intend to game then go with an E7200 instead, almost the same speed for less then 100$ when it comes to daily tasks (word processing, web browsing, etc).
What DO you intend to use it for?
I ordered a Q6600 to replace my E8400, should arrive soon. Others swear by the E8400. It really all depends on what tasks you perform.