A 10 inch drop in screen size is pretty dramatic when looking at these size ranges.
The Bravia is $700 more for a considerably smaller tv, so think about size here.
Since you were looking at the LCDP first, I gather you have no intention of mounting it on the wall, therefore it shouldn't matter if the tv is flat or not, right? Granted, the 32 might look better picture-wise, but what good is that if you can't see it very well?
When I'm in work next I'll take a look at them and see what I think. Also, a good thing you could do is look up the specs on both tv's and get the resolution, contrast ratio, etc. I'm going to do that soon, just so I can know exactly what they are. I don't go over to tv's that often, so I don't know too many individual specs on them. (I stay mostly in Audio).
~Chuck