Speaker shootout question -- do you position the same or differently, depending?

Dispersion pattern will be a major consideration regarding speaker placement. 

Why wouldn't you want to hear each speaker to full potential in your room? Absolutely, move to preferred location for each speaker. Per above, dispersion patterns different for different speakers.

I agree with finding the optimal position. I agree that any one pair should be removed to get out of the other pair's way. 

Johnny, not sure what you mean by "The room dictates the best position not the given speaker" since it would be room-AND-speaker, right?

Generally, the room will dictate where the speakers will be placed within the room, to deal with peaks, nulls, modes, etc.  Once they're in those positions, then speaker toe and rake angles can be experimented with to dial in each given speaker pairs soundstage, focus, etc.

Ideally the speakers should be compared in their optimal sounding position assuming this is a position you are willing to live with. 
 

In my case, the system/speakers reside within the main living space and therefore have to sound good in the space allocated to them. Fortunately, I can place them at least 3’ out from the front wall and at least 6’ from a side wall. So far, this location has worked pretty well for 2 different floorstanders and 2 different bookshelves.