They cut very differently, in my opinion.
In Edwin's case, I'm not sure that "trained" at A&S is exactly the right description. He adopted the A&S style, cut it at A&S for years, and continued to cut it when Steed was formed.
Rather than give you my impression, I'll quote an old Manton post from eight years ago:
Originally Posted by Manton
I was generally happy with Steed. My first suit surprised me: it was dramatically different from anything I had ever owned. There is no mistaking it for anything but a bespoke suit. The silhouette is not exaclty subtle. Swelled chest and very pinched waist. Curved, "belly cut" lapels. Edwin also makes something like a true natural shoulder "drape" suit. One difference, however, is that he does not extend the shoulderline, but ends it right on the deltoid. There is almost no padding. The shoulder seam cants backward; the "backneck" or "pupilla" measurement is a perfect 3". The chest cloth truly "drapes" from the shoulder seam. Hard to do well. The coat is very, very comfortable. And it really "sticks": you can flail your arms in all directions and the collar of the jacket will never lift so much as a millimeter off the back of your neck.
Keep in mind that at the time that Edwin and Tom were at A&S, there were several senior cutters, each with their own take on the A&S style. It wasn't as monolithic as it is today.
Also, Edwin was at Nutters. It is my opinion that his days with Sexton also influence his cut.
There's overlap today between Tom and Edwin, but their centers of gravity are not the same. That's how it should be.