Are you "supposed" to let things die before you pull them out of the garden and put them in the compost? For example, tomato plants. When they are done and no longer producing, maybe beginning to brown, Go ahead and pull em out? I noticed lots of people leave their cornstalks in the ground for a LOOOOONG time. Is this better? Is it putting something back into the soil, or is it laziness?

As a general rule of thumb, what do ya'll do?

Then, when it is "fresh" plant greens is it high in nitrogen (as far as composting is concerned) and when it is brown it is lower? Or am I completely off base?

There are no rules for pulling out spent plants. Depending what they are, I leave some that have seeds for the birds. If you have diseased plants, definitely remove them and burn them somewhere other than your garden. Anything left in place is just added organic matter for next year. Some things I crumble up and just let lay where it falls, then cover the whole works with grass and leaves for the winter.

Generally speeking, there are 2 schools of thought on this. You have shown knowledge of both. which you choose is entirely up to you. While pulling the plants while green, you ARE adding Nitrogen to the compost bin (which helps out all the garden that you add the compost to). But in leaving them be, the nitrogen (as well as some other trace minerals) gets put right back where it was drawn.

As far as "lazy" goes, yes it is, but then so is mulching. And both are better than all that weeding (and the spraying that chem gardeners use).

this is a recent thread, bumping so others can reply.

For the most part I put the dead, or dying, plant material right back into the soil where it was growing, I see no good reason to haul that to the compost pile and then a while later haul it back. Many times during the growing season I will take cuttings/prunings from different plants and put that into the compost but the end of season stuff just goes into the soil where it grew or into the mulch where it grew.
There is some research out there that shows that putting that plant material right back can aid greatly in suppressing any disease pathogens in your soil.