Your statement isn't actually too clear. If you are asking why is it clearer on your 1080p LCD it is because it's 1080p. Your plasma is probably 720p and can ACCEPT a 1080i signal, but it will downconvert it to 720p, so you loose the higher resolution.
Plasma's are 1080p or 720p, not 1080i. So check your plasma's documentation and I think you'll see it's 720p.