You will find fanboys on both sides, but nowadays, both are very good, but not perfect. Either will give you a very good picture.
Plasma has an edge with black levels, (lack of) motion blur, and is a bit better in dark rooms (lower ambient lighting). Can get some IR (image retention, *not* the same thing as burn-in)
LCD's are brighter, are better in bright rooms, but have worse black levels. Less prone to getting IR. Uses a little less power then plasma, but is usually a bit more costly to buy compared to a similar plasma set.
Best thing to do is go to the store and look at both models in as close your home lighting as possible, and take the TV's out of store mode (AKA "torch" mode, which has maxed out brightness and color) to get a realistic picture similar to what you would use at home, then let your eyes decide what looks best.