Others can voice their opinion, but you may as well go back to the source they always refer to: dbltree aka lickcreek aka Paul Knox
His advice was
Cereal rye is always my first choice over wheat or any other grain because it is higher in protein, requires no fertilizer, will grow on low PH soils, has alleopathic chemicals that discourage weeds, is a nitrogen scavenger and a root system that breaks up soil hardpan and improves soil.
If you want mine the wisdom of 64 pages of talk about cereal grains and cover crops go here
https://iowawhitetail.com/forum/threads/cereal-grains-and-cover-crops.15879/
Edit: Wow just noticed the photobucket crap is on dbltree threads on that site too. A real shame since he took lots of pictures with all his time to do the explanations. His tree planting thread was another good one that is getting that stuff too but has some other pics that do show.