Wow! A real projector question! Quite rare for these forums.....
The PTAE4000 is a great projector for the money, and has some useful features which will suit some people, and is a better projector at the £2k mark than you could pick up for £5k a few years ago. But, the HC7000 is a superior projector. I've mentioned before that the HC7000 has a more three dimensional picture (depth, whatever you want to call it) compared to many of it's equivalently priced competition (and some more expensive ones), produces a sharper picture, runs quieter, and is a better built projector. It also looks a little cleaner too, with slightly less noise, which helps produce a more convincing picture.
It's worthwhile having a peek at both of them if you can to see what you think.