Click to enlarge. SO close
I have to start here, because this Epson was our Best in Class winner in the heart of the 1080p projector price range. It's replacements are due out next month (December), but until then, the 1080 UB remains a good "standard" to compare against.
The Epson is the brighter of the two (roughly 21%) in best mode, and significantly brighter in its brightest mode (slightly over twice as bright) giving it an advantage for those wanting larger screens. The Epson was the lower cost king of black level performance, and the two are pretty much equal in black level performance.
The HC7000 (link to specs) has the advantage in terms of "film-like" imagery when watching movies. The Epson image seems just a bit "hard" looking by comparison.
In terms of sharpness, while the Epson is fine, the HC7000 is definitely the sharper of the two, and you can best appreciate that on all digital source material, rather than film.