I think from what I have seen the rye works well as a cover crop in areas where it is traditionally very wet at planting time. Rye seems to suck a lot of moisture from the ground and does make a mass of vegetative material to mulch between the rows.

Wheat won't suck as much moisture out of the ground which may be good or bad depending on what you are trying to accomplish. Wheat will not have the amount of surface vegetative matter but it does have a better root mass than the rye....Wheat probably kills easier than rye.

On the other hand rye when it is green does strip till nicely if caught early. Probably better than green wheat.

Here's a video of strip tilling into a rye cover crop which had been sprayed with Round-up but is still very green as you can see.click on "HQ" in the lower RH corner to see better.

Jim at Dawn