The reason I went LCD over Plasma is screen burn. I'm pretty sure your desktop would burn in to the screen within a year or so with a plasma. They're also very sensitive to movement and should never be tipped up.
In regards to the OP, I would say yes, you would notice a difference. One if the things I like about running 1080 is you can run out of native res without it looking crappy. I play Crysis @ 1440x900 and it doesn't look too bad at all. All other games I run at full res and it looks totally awsome