The whole thing is confusing--Harry Kim is listed as the Chief Operations Officer on Voyager, which ran separately from engineering. The same with Data on TNG.
Obrien is the Chief Operations Officer, yet all he does is engineering.
He has to be a chief engineer of some sort, because he is the only officer giving orders in engineering when he is on the Defiant.
And yet he isn't called an engineer.
Because of all the techno babble, I think Geordi was the nerd's engineer, and Scotty was the Sci Fi's engineer.
One particular thing I like about Geordi was how we got to see him grow throughout his time on the Enterprise. Scotty didn't have that advantage.
Geordi is one of my top favorite characters, but Scotty is one of my top favorite engineers. No matter which way you flip it, Scotty would get the top award.