A lot of great replies in here. One thing I would definitely underscore is something Mike Jay first brought up — water usage. Out here with our sandy soils and dry summers, weeds can quickly decimate other crops around them. They will germinate in a thick mat in the spring, go to seed in a few weeks as the rains stop, suck up all the water in the area, and die off — months before your veggies will have had a chance to mature. If I forget to irrigate for a week, weedy places will be completely dead, while weeded places will be doing just fine.
If you rob the bank and the getaway car stops at the compost pile, and the finished compost goes back on the garden, is that good, better or worse than dropping it?
I think this is one of those places where you'd have to really work on defining what you mean by good. I make compost to breed beneficial organisms, and a compost pile will do that orders of magnitude better than mulch will. At the same time, my compost pile is burning up the fuel that these beneficial organisms need to survive — the same organisms that live in your garden soil that might be able to use that fuel if it were chopped and dropped. At another look, a compost pile can heat up enough to kill unwanted seeds, while chopping and dropping will just leave the seeds in place… I guess I look at it all as a complex equation without an easy answer.