There's a couple reasons for this. The primary one is that the 15-inch display is condensing the resolution of the BD to a MUCH smaller space, so it appears to be sharper. When you spread it out over a larger area, the image is naturally going to seem softer.
However, the LG is a very sharp and very bright projector so make sure the setup details on projector and BD player are correct. Go from the obvious (using HDMI cable to connect the two) to the not-so-obvious (ensuring that the BD is putting out a full 1080p resolution). Also, the LG has good but not outstanding black levels, so tweaking the brightness and contrast settings, along with the sharpness control, may get the image to more fully suit your taste.