[dice]

Winter rye decomposes at about the same rate as straw (in fact one can
buy rye straw some places that sell wheat straw, oat straw, etc). Hairy
vetch decomposes more quickly (a lot less cellulose, more nitrogen
in the top growth). Winter rye does a better job of filling the soil with
roots and preventing erosion, and it recycles nitrogen that may have
been left over from the previous crop, releasing it more slowly as it
decays than vetches.

When growing winter rye alone, I usually mow it and use it for mulch
rather then turning it into the soil. It is tall, stiff, and awkward to turn
in with a shovel. It also has allelopathic effects on small-seeded weeds
that may interfere with direct seeding of some vegetable crops if it
is incorporated into the soil before seeding. (No big deal if you have
a plow, where you can just cover it with a layer of dirt and seed in that.)