What IS your usage? Why do you need portability? What level of quality are you hoping for?
Micro projectors are, IMO, still a toy. Their image quality doesn't match up to those projectors designed for home theater and reviewers basically never compare the two side-by-side for this reason despite the mass of people on this forum who do use them for that purpose.
Home theater projectors, in contrast are bright enough to deliver a very punchy image on a screen size of about 92" to 133" diagonal rather easily. Their lamps do need to be replaced, but can generally last 1-2 years for most people under normal usage. They have enough light output typically for good 3D viewing if that's something that interests you, but more specifically, they have better shadow detail, better optics, more placement flexibility, better contrast, better motion handling, and greater image uniformity.
So, the 770ST has five times the rated brightness of the PA75U. That's not a trivial amount. For that, the list price is less than the LG!
It certainly isn't your only option though...
All of those models are ones which I would strongly consider for home theater use depending on my specific setup.
That said, if I wanted a toy for the kids to play with which I didn't want to see damaged, or I was a person that regularly wanted to carry a projector with me for travelling and I DID travel a lot with need for a projector, or if I wanted to leave the projector on 10+ hours a day, then I might consider the LG or a similar model. But, all of those situations are far and away removed from typical home theater usage. Especially for a good home theater setup with surround sound and the rest.
If your home space is good enough, than it certainly warrants the jump to $800 and the Optoma 131x projector or similar.
So, there is still a lot that you should talk about in regards to what your actual usage and what your specific needs and goals are. There are times where micro projectors make sense, but those needs tend to be very limited IMO.