In my opinion the resolution you need depends on viewing distance and screen size. These will detemine the visibility of screendoor effect and pixilization and how much fine detail you can see. Screendoor effect is caused by the pixel fill factor not being 100%, the gaps between the pixels form a grid, the visibility of this grid is the screen door effect. Pixilization is caused by the image being made up of alot of squares.
Screendoor effect can make an image unwatchable, if you know the pixel fillfactor you can calculate viewing distances the same as for pixel size by using the size of the gaps.
Rafabamad says screendoor effect on the Epson HC720 is evident at 1x screen width viewing distance.
http://www.avsforum.com/avs-vb/archi.../t-917897.html
For pixilization I use
http://www.1728.com/angsize.htm to calculate the angle size of a pixel using the size of an individual pixel (screen width / number of pixels (1280 for 720P high definition) and the viewing distance.
Average visual acuity in ideal lighting of ideal material (black and white lines) is 1minute of a degree. Contrast sensitivity(the size of details that most determine the perception of sharpness) peaks at 1/3rd - 1/7th of visual acuity. To avoid visible pixilization (looking at a black 45 degree diagonal line on a white background does it look like a staircase of a smooth line) I would say you want the individual pixel size to be smaller than 3 minutes of a degree. A still black and white image is a worst case situation for pixelization. So in normal color moving images you are alot less likely to see pixilization.
Visual acuity average in ideally lighting is 30 line pairs per degree (line pair =one black and one white line) but can be upto 45 line pairs per degree depending on how good your eyesight is. This means with average eyesight you can see details as small as 1minute of a degree of your visual arc. This has been taken to mean you want to be able to see the individual pixels to get the benefit of the resolution, as in
http://carltonbale.com/2006/11/1080p-does-matter/ But visual acuity in less lighting, moving objects, and of contrast in colors is alot less. Since you want to see the image as a smooth image (not a checkerboard) this is no bad thing.
Vermier acutiy ability to notice a line is not straight but offset is 10x visual acuity. So higher resolution still improves things on the large scale, making the image even smoother even when your eyesight can not resolve smaller objects.
As a side note the projectors you mention use different technologies, the Epson is a lcd projector and the Optoma is a dlp projector, both technologies have their own advantages and disadvantages.
