I've used the LPI quite a bit, but I've never seen an NexImage, so bear that in mind.
From what I've read the NexImage is very similar to the ToUcam webcam modified for use on a telescope; primarily removing the lens and adapting the case with a 1.25" barrel. Sooo, the NexImage is comparable to buying a ToUcam already modified and ready to use and it's operated in the same way; you capture videos of the Moon and planets using third-party software, strip out the best images from the image stream, stack and average those. I haven;t seen very many pictures taken with a NexImage, but I have seen many taken with the ToUcam and they're excellent so I'd assume you can do similar work with the NexImage.
Now for the LPI. The LPI is similar in that it uses a small CMOS array (an array similar to a CCD but operates on a slightly different principal) and you connect it to your computer via a USB cable. There the similarity pretty much ends. The LPI is not a modified webcam but a webcam-like camera designed specifically for astrophotography and it comes with software specifically designed for that purpose. Instead of taking a video stream it takes individual pictures which are normally selcted, aligned, and stacked in real-time using the LPI software, though you can save the source images individually for processing with the image processing software that comes with the camera or other third-party software like Registax. Personally, I let the LPI software do the stacking and I just use Registax to apply some additional sharpening to the final image.
From what I've seen both cameras are very capable of producing high quality images so you'd probably do well with either one. The LPI came out before the NexImage so I ended up with an LPI and I'm very happy with it. It's a turn-key system that I routinely use to take high resolution images of the Sun, Moon, and planets and I've also used it to image asteroids as faint as 12th magnitude.
-John