I´m a bit bizarre when it comes to demo/lite/free. I don´t like those namings and pretty much avoid such.
Then again, I only buy indie game, it has been more then 10 years that I actually bought anything main stream.
I think IMHO, that the way to go is to have the lite version as a full smaller game, possibly with a bit different story, but with uniqueness enough to go like a full game.
Back on the amiga days, there was this isometric game called cadaver.
2 or 3 unique demos were released prior to the game, mostly on cover magazine´s disks.
They were kind of lite versions of the final game but only shared the engine, gfx, and the story took place on special ocasions prior to the story of the final game. Those levels were actually not inside the final game at all.
So those were unique games, I can call them a rare collector´s piece.
The one that came on the CU amiga magazine(last supper) was different then the one on ONE magazine.
I like this approach better, IMHO, a demo/lite cut down version of the final is offending (for a bizarre user like me) while a set like I said, makes it unique.
At the end, it isen´t much different from a free version, it is just that its uniqueness makes it also a required download for those that bought the final version and enjoyed it and I think it could promote the whole brand a lot more. It will provide a few extra work to the coder, but should I be working on a bigger game myself I would follow this path.
Take a look at the internet about cadaver, see if you think it is a good idea.