For engine start and After Start Checklist, usually I have the FO display the engines on his side since he’s starting with the Hydraulic and Flight Control displayed on my side. After that, I prefer the engines on my side for takeoff even when I’m the PM since it’s my decision to reject or not. Once airborne, the FO as the PF can have the engines back on his side while I get the big map display back. Talking with my FOs it seems this is the way many captains do it.