I have the B17 Imperial and the B17 imperial S. I measured for you and they both are 175mm wide at widest part and the distance from the rear to the widest parts is about the same. so the difference in length is all in the front part.

the reason i bought the S was stupid, it was to avoid a dropper on my fatbike, lol. It didn't help, and i got a dropper anyway.

I believe the S is targeted towards females, so not sure if that is a good choice for me (male) anyway. they feel the same or similar. the downside of the S is the rail is short and you have almost no for-aft adjustment. this is why i will replace that with a proper B17.