These are not really comparable and for many reasons. One of the largest has to be that the content you see at the cinema is no where near the quality of what you get at home via a set top box and blu-ray. The resolution, bit rate, color bit depth ect is all substantially higher then what you get at home.
That's the content, but I think you're more referring to HDTVs versus DCI digital projectors. This is also similar to what I was talking about before regarding content. These projectors are built for a completely different purpose. These projectors don't usually have the luxury to reach on/off contrast ratios like most HDTVs and other displays do. A lot of that has to do with how bright they are/have to be. That's really the only negative caveat about DCI projectors. The rest of the issues most people complain about when at a local cinema has to do with how the projector has been setup or calibrated. This is usually due to poor management. In all other areas I think that digital projection in general is vastly superior to any HDTV that I've seen. These DCI cinema projectors in general will give much better picture quality then any HDTV regarding color accuracy, larger color space, sharpness/resolution, native motion, motion handling of the content, and gamma.
That's regarding DCI projectors, now if we were to talk about non commercial home theater projectors there are TONS that trounce the PQ of 99.99999% of all HDTVs. They can be expensive though. To this day the only HDTV that I would own over a projector would be one of Pioneers latest generation Kuros. There are size limits to those panels though. 60" isn't very large compared to todays HDTVs and very very small when compared to a normal image size coming from a projector. There are a bunch of single chip DLP projectors out there under $10000 that I think outperform every HDTV currently being made today.
I think most people who frequent this subforum would agree with me. My father owns a ~60" Sharp Aquos LED LCD HDTV and my brother owns one of the more expensive 50" plasmas from Panasonic, in my opinion none of them come close to overall image quality to any one of my three projectors; the Marantz VP-11S1, NuVision ProVu P2, and Planar PD8150.