Having just started having to orbit to the right after 15 years of going left, I can report the following.
I find myself getting too involved in what's going on on the ground outside my window, because there's only one bobby in the aircraft who can see what's going on down there, and I want to/am expected to help him out. Yes the other guy has the camera, but it's not the same. Turning left, there are two bobbies looking out, instead of one. The camera isn't required all the time.
The "Send Position" function that the newer a/c have with the map/camera is excellent when it works. Ours wasn't working the other night. The efforts of the rear right hand bobby trying to get the front left guy on the camera on to a target on the right just weren't working because the guy on the camera couldn't look out of the window and see what he was looking for. A quick re-position to put it on the left solved the problem.
I have to keep looking back the other way, to check instruments and the front screen to see what the camera is looking at in order to position the a/c accordingly. Turning left, I can see all that naturally.
Not had a pursuit yet, but that's probably the only situation that I can see that having it on my side would be better.