Not quite.
The e still doesn't have the electro-hydraulic 3pt hitch control. That's a HUGE difference, especially if you've ever tried to hook up to a hay mower by yourself, etc. And, there are still mechanical differences, 3pt hitch lift capacity, engine performance, etc.
The M is still a "premium" tractor, and the e is an economy. You can't make a silk purse out of a sow's ear.

And, the OP stated that he wanted a tractor do work a "hay operation." That's what I do. I chose the M and still think it's the best choice for the intended purpose.