I am planning to print my first PC item today.
I own both Bambu’s smooth PEI (“high temperature”) and engineering plates.
Can someone, experienced in printing PC give me a hint what the pros and cons for these plates would be (only related to PC printing, please).
Thank you in advance!
PC is my go-to filament for tough mechanical parts. If the part needs threads, you can tap them directly into PC and still get about 90% of the strength you would get from heated brass inserts. I use the older dual side engineering and high temp plate and honestly haven’t seen any difference between the two surfaces.
My best tip: put down a very thin layer of glue. It sounds backwards, but the glue works as a release layer and helps the part pop off the plate instead of trying to fuse itself to the plate surface. PC grabs onto the build plate with the enthusiasm of a caffeinated raccoon and I’ve damaged plates before learning this trick. Textured PEI works too, but use a bit more glue.
Any glue works, but white paste is the easiest and in my view, at $2 a tube, best value. A little discussed secret the printer companies don’t want you to know. The white glues are exactly the same substance used in childhood school glue sticks. They are even made at the same factory, except when they put the word “3D printing” on the label, somehow the price goes up 3X. 
After you apply on the white paste glue, then with a very wet paper towel, spread a thin, even layer. I also use a marker style applicator that I modified to dispense hairspray. It coats the smooth plate beautifully, but white glue does the job just as well.
Avoid the liquid glues like Bambu, Elegoo, Magigoo, BIQU etc. They are all $19/bottle and they all come from the same factory, you can tell by the shape of the bottle. They are sticky syrupy disasters waiting to mess up your first layer. I have both the Bambu version and have discarded the others and after 3 years, I still have half a bottle of the Bambu stuff on the shelf. Plus, the bingo-card-marker-like applicator dries out very quickly and has to be regularly cleaned.
Also steer clear of the wildly overpriced Nano Polymer. I got a bottle as a gift and at $45 for 120ml it’s about five times the price of a decent single malt scotch and very disappointing as performs no better than basic paste glue. And I’m confident it tastes worse… than the single malt that is… 
The sole application where the Nano excelled was use on a Garolite (G10/FR4) plate where I was printing nylon.
Thank you for the “very comprehensive” answer! 
So, I did print PC on my Prusa before but with totally different build plates and glue stick is what I always used anyway (and all Bambu manuals say to use glue stick for PC).
So just to make sure I got everything needed from your post:
I can both use Bambu’s smooth PEI (“high temperature”) and engineering plates and it will not make any relevant difference.
Correct?