First off let me say I have tried using a laptop in a live situation, so I have a bit of experience with a laptop and an MPP.
Laptops are good for a lot of things, and are okay if all you want to do is play midi files, MP3's or set up songlists etc all of which can be achieved using simple to use one-off programs (winamp, media player to name just 2).
But imagine trying to have all these things going at once, midi file player, a song list, a viewer for your charts,an audio file player etc etc and then getting them all to be performing the same song at the same time on one device and it gets quite "awkward" to say the least in a live setting.
Now there are programs that can accomplish this but at a very hefty price, that then must be added to the cost of the laptop.

As to the practicalities, I have found it's a bit hard to turn pages using a mouse when playing a keyboard with both hands.
Also a laptop has a much larger "footprint" and is more tricky to place in the ideal spot for viewing charts (without blocking your face) when playing live, whereas the MPP has a much neater profile, much easier to position where you can see it and the audience can see you, and is exactly the same as using a music stand and pages can be turned by use of a footswitch.

Try turning a laptop around by 90 degrees , bit hard to read hey? Or try turning pages without a keyboard or mouse?

Plus the MPP has a touch screen which does make it rather more practical for live work. Plus it will also play and store MP3's..
And for the price of an MPP yes,you will maybe get a decent "Budget" laptop, but not the "best one around with money left over" And you certainly do NOT want to buy a second hand laptop for many reasons that I will not go into here.
Also pretty much all laptops have noise issues when trying to run audio from the inbuilt soundcard (even the MPP does), so an external audio interface is required.
Plus try dropping a laptop from the height of a music stand whilst the hard drive is running and see what happens.
There are a few testimonials on the MPP forums about owners dropping their MPP, or having them knocked over by punters, and they still work perfectly.
I am not trying to tell people what they should use, just that the MPP has a vitally useful role in my live setup. A laptop is perfect if you want to only have a device for storing songs to just play without having to read anything on the screen as you can place it at your side or behind you etc etc. In my setup the keyboard stores all the data for the songs, MP3's, WAV's Midi's, and all my charts appear on the MPP. To me it is an elegant and ultimately practical setup and worth every cent.
Dennis
PS sorry for the long post!!!