Please be aware, that in general, CF-filled filaments for FDM have the fibres chopped in very short pieces. Those pieces easily get detached from the surface of a print and get stuck in the skin of your hands. I have seen 3 different tests, that showed the same result.
I have no idea, what happens with those pieces. The testers also couldn’t say. Maybe they just fall of, maybe they migrate into your body. That uncertainty for me is sufficient to mostly avoid them and only use them when the application makes it really necessary. This might change when somebody shows that they are harmless.
On the physical properties:
Mostly those carbon fibers increase stiffness and reduce shrinking which in turn reduces warping. That is why usually soft materials like PA get much easier to print with CF. In addition, many materials have an increased temperature resistance with CF.
At the same time, impact strength and layer adhesion is reduced by the fibers. As far as I know only long fibers really can increase the strength in the XY plane.
If by strength you mean stiffness, then yes, it improves with CF. If strength is the force that you need to break something, then most filaments actually are weaker with CF.
Regarding PLA-CF: I think the benefits are purely cosmetic ones: You get a very very matte and quite rough surface that conceives layer lines almost completely. I think it has a very appealing and high quality appearance. As PLA is already very easy to print, I didn’t see much difference in ease of printing. I get along very well with all PLA basic, matte and CF at default settings. Temperature resistance is not improved as far as I remember.
I’m not surprised that Bambu compares it to PLA matte. That probably is the closest alternative. I have measured layer adhesion of basic and matte PLA from Bambu. Matte did break at ~ 1/3 the force needed for basic. I guess that PLA-CF is somewhere in between. Since the findings I wrote above, I got rid of all my rolls although I really liked the surface a lot.
I have one roll of PETG-CF that I still haven’t opened since buying it, so I can’t give first hand experience. I think you can expect reduced warping especially on an open printer as well as much stiffer parts than regular petg. I could imagine that temperature resistance is improved. But you should find those information in the data sheets.