Panasonic PT-AE1000U vs. Optoma HD81
This is almost a classic LCD vs. DLP. The Optoma is definitely brighter, and can handle much larger screens, but costs more, and the Panasonic clobbers it in placement flexibility.
On the other hand, the street price of the PT-AE1000U is more than $2000 less, so these two are hardly competitors in terms of price.
The PT-AE1000U, is far more likely to work in your room. Most people considering the HD81 will have no choice but to ceiling mount, for the projector has only a 1.2:1 zoom, and no lens shift. Even ceiling mounted it is especially limited in placement.
The Optoma HD81 should have a slight edge in sharpness over the Panasonic. I was extremely impressed when viewing the Optoma HD81 at CEDIA, doing Phantom of the Opera from HD-DVD.
The Optoma comes with an outboard processor that stays with the rest of your equipment, and has a single cable that runs from the processor box to the projector, carrying all your source selections. The HD81 has more inputs than any other projector in its class, so far.
Due to the pricing difference, these are only competitors in that they are two of the few 1080p projectors under $10,000, the Optoma's real competition is the previously mentioned BenQ, while the Panasonic's is the Mitsubishi.
As I finish reviews of other 1080p projectors you can look to the summaries there for updated info on how they compare.