George,
Both are excellent projectors, especially for the money. This is really a no lose situation as your friend would/will enjoy either one.
The 4805 is more of a plug and play projector as it will come out of the box pretty much set. The H31 needs a bit of tweaking to get its picture to look best.
Imo, the H31 has a bit more pop to its picture. The colors stand out more. Depending on your view, this may be a positive or negative?
Lastly, while the blacks on the 4805 are very good, I thought there were better on the H31.
A positive for the 4805, it has better bulb life.
As previously stated, both are great so maybe costs will be the deciding factor?
Regards,
Jeff