This has to be qualified by the Lens Memory feature. That in its own right is a plus for the PT-AE7000, but, that advantage goes away, if you, like most stick with a typical 16:9 screen. Here, we look at other aspects of placement flexibility:
Zoom ratio: A slight edge for Epson, with it's traditional 2.1:1 vs. the Panasonic's 2.0:1 zoom. Basically the Epson can be placed anywhere the Panasonic can, but can be a little closer or further away from the screen if needed.
Lens Shift: Both offer vertical and horizontal. As has been the case in the past, the Epson offers slightly more lens shift range.
General Features: PT-AE7000 vs. Home Cinema 5010
CFI - Creative Frame Interpolation
I've always considered Panasonic's CFI to be one of the best out there. I've seen smoother, on some Runco projectors, etc., but the PT-AE7000's is smooth, and is one of the best if you insist on running CFI on film based movies. I don't, as I don't like the "soap opera" effect at all on film based movies, but I do like CFI for sports.
Epson's CFI is also smooth in it's Low setting, but I have to give the Panasonic the edge. For sports, between the various settings the two projectors offer, let'c call CFI a draw. Thus, overall, a slight advantage for the PT-AE7000 in terms of Creative Frame Interpolation.
Epson offers a number of predefined gamma's and an easy method to customize your own, based on visual adjustment or by the numbers.
Color Management System
Both have good ones, no advantage we can see.
There are more features to discuss and we will attempt to add a few more. We conclude with our final take on which projector best meets the needs of different people. It's all about trade-offs, for, as you see, neither projector is really superior, overall.
For 2D in general, I have to pick the Epson Home Cinema 5010 [ if you would like WirelessHD, the 5010e], as the better choice for most folks who are primarily or completely into 2D. For $300 less than the Panasonic, you get a somewhat brighter projector, with better black levels and more pop on those darker scenes, and a better warranty.
For 3D in general, the advantage goes to the Panasonic. The Epson's lack of a dynamic iris function, CFI and Super-resolution - the primary dynamic features, gives the Panasonic better blacks, and if you want it, smooth motion. I also noted that in 3D the Panasonic sharpening seems to be working, while Epson's Super-Resolution doesn't. That results in a touch sharper 3D image for the Panasonic.
You, however, have to match to your situation, and tastes. Obviously, in general, the Epson Home Cinema 5010 has a brightness advantage that can translate into a larger screen. And don't sell it's warranty and support advantage short. It's 3D is at least as bright as the PT-AE7000 but it comes up short in blacks and 3D CFI. Since blacks are less critical there (already a bit dark), and CFI is questionable
The Panasonic PT-AE7000 has the convenience of motorized zoom and focus, (a nice touch), although in most cases these projectors get mounted, in which case, you aren't zooming or focusing (unless you are using an anamorphic screen and Lens Memory).
Finally, for a few of you:
Those two key special features I discussed earlier - Lens Memory, vs. Split Screen, can determine your decision, all by themselves. I say that because, while we can talk out which projector is truly better, they are both very good ones, and more similar than different.