APS-C sensor ratio & Face Recognition Focus

Many of the Canon EOS cameras I'm also looking at have the APS-C sensor which turns a 50mm prime lens into an 80mm equivalent focal length.
How does the BMD CC 2.5k sensor compare to the APS-C sensor in this regard?
Will the BMD CC 2.5 EF mount with an EF 50mm lend give me a 50mm or an 80mm equivalent or something in-between?

One other question, the EOS cameras have the "face recognition auto focus" feature built into the camera's software. I know that in some situations, auto focus will be required regardless of which system I choose (BMD CC vs. EOS body) but it occurs to me that with the EOS body, that "face recognition auto focus" might come in REALLY handy, keeping the focus on the actor and not the background in a run-and-gun shooting situation.

Does anyone have thoughts on this?

Thanks in advance,
Chris

a 50mm on the BMCC would crop to the same frame size to about the same as (roughly) a 115mm lens (x2.28) the lens though will still have the visual characteristics of a 50mm. As for Auto focus. The BMCC is not about auto focus and face recognition as it's more of a cinema style camera and most things are done manually so learning to keep focus and planning your shots out are the order of the day instead of just run and gunning blindly (There are though some simple techniques to keep the actor in the focus of the shot whilst lots of movement is involved involving string or straps or wood or gaffer tape) Also face recognition can be a nightmare in run and gun shooting. I for one prefer the control I get with cinema cameras over auto features. If you feel the need for for these things then the eos cameras are for you.

When compared to a full frame camera the crop factor for ASP-C cameras is about x1.6.
So a 50mm on an ASP-C camera gives you a similar field of view as an 80mm when compared to a full frame DSLR like the 5D (as you stated)

The crop factor of the BMCC (EF and MFT) is about x2.3.
So a 50mm on a BMCC gives you a similar field of view as an 115mm when compared to a 5D.

The crop factor of the BMPCC is about x2.8.
So a 50mm on a BMCC gives you a similar field of view as an 140mm when compared to a 5D.

The BMCC does not have auto focus. Auto focus is not something that is found much in the professional video market/film market. It's also not very common on DSLRs. Even the 5D does not have auto focus in video mode.

The BMPCC does have push auto focus when using electronic MFT lenses. It will focus on the object in the centre of the screen when the focus button is pressed.