Generally speaking: And this varies with each particular vessel, since some have quirks and vary from the norm. And this applies only to tugs, since they have larger rudders than traditional vessels.
It has been my experience that inboard turning wheels have better thrust ahead but aren’t as good backing. They don’t twist as well. However they walk like crazy.
Outboard turning wheels back like crazy, and turn better going ahead. But they don’t walk at all. (Some times you can overpower the backing wheel and sort of crab sideways ahead though.)
The conventional thought is to use your outboard wheel when turning to ‘help’ you through a turn. Sort of like having the ‘lever’ further outboard to help the vessel turn.
The evidence on this is the outboard turning wheels allow you to use the outside wheel (E.G. port wheel when turning to stbd) so the traverse thrust of the wheel will help ‘walk’ through the turn. On an inboard turning vessel when turning to stb (previous instance) using the stb wheel is sometimes better to turn with.
To check this out, in either type vessel, when going ahead back one wheel full, just so the wash is coming out the side. Go to each side quickly and watch the results. On an outboard turning wheel all the wash will come out on the side you are backing on (sometimes at about 45o angle to the hull. On an inboard wheel some of the wash will actually cross over to the other side of the boat.
This is why some boats will back well when put astern, and some will immediately start to twist as you back.
Then other mention that k-nozzles negate the effect is not true. K-nozzles may reduce the effect, but it is still there.
My experience on this is twofold. I worked on a triple screw tug. port and center right turning (inboard), stbd left turning (inboard.) Backing both port and center screws the boat would go straight back, back the stbd would pull the boat to stbd. Backing just the port would pull to port.
Also at another company they had a k-nozzle boat. While re-engining the resident rocket scientist in the office ‘heard’ that since it had nozzles it didn’t matter which rotation the props had. So he ordered three (port, stbd, and spare) right wheels. The boat was a death trap. On her first job with a loaded barge the operator took out a dock, doing an easy, often done right turn out of a berth. Didn’t twin screw for crap! When he backed it backed to stbd, pulled the bow further into the dock too! They lifted the boat out the next morning and had a left wheel put on ASAP. Problem solved!
Your other question about bollard pull is negligible either way, however it is the K nozzle that provides the great increase in pull. Maneuverability is sacrificed by K nozzles though. That is the trade off, nozzles = more bollard pull, but open wheel are more maneuverable.
Anyway, I hope I haven’t further clouded the issue, but I am sure there are others with different opinions, and I am sure some who aren’t even aware of these small differences. Sorry for the long ramble.