I presently shoot with slide film and project the images. I am considering digital. I would like to continue projecting the images via TV or digital projector. Which sensor would perform better for my projection needs? APSC or full frame?
Either should be fine - typical DSLR resolution is still a lot higher than typical digital projectors.
There's always the option of having slides made from your digital files and using your existing projector. That might give you higher resolution.
Typical consumer TV and projector is around 1080P i.e. 1920 x 1080 ~ 2 MegaPixel(MP). A 4K TV is ~ 8.3 MP. And 4K projector will be pretty expensive currently.
So current consumer range 8 megapixel digital camera is sufficient.
Full frame DSLR will make no different in your 4K TV/projector, after all , it is all about shooting skill.
OTH, if you are talking about converting film to digital, then 20MP film to digital converter will persevered more details. HOWEVER, it make no different on the digital projector/TV due to current projection pixel limit.