Be careful on the native resolution of the projector. Many LCD based projectors are 4x3 not 16x19 and get the wide screen format by using less of the LCD display. DLP projectors do have native 16x19 format. Make sure they support the full 1080p resolution which I believe is 1920x1080. You also want to get the most Lumens you can. An LCD will typically get higher lumens. In either case, none will be as bright as a TV. Refresh rate should also be considered. Many projectors are designed for computers so 60 Hz is typical where you can get 120 Hz on newer LCD tv's. The projectors you see in the $1000.00 range will probably not compare very well to the performance of a flat panel, you probably need to step up the a $2000 dlp projector.
As for comparing to a LCD or Plasma display, if you have a room with sunlight your projector will not match the brightness and contrast of a TV. They key benefit of the projector is screen size for the $.
Unless you will have a dedicated room with low light for your projection tv (like a screening room) I lean towards a flat panel lcd tv.