Going the computer route, you also to be concerned about is the user interface and portability. With the computer you need to use the mouse or computer keyboard to select sounds or styles, or adjust tempos. This is not a problem if you are using it in a studio, but when playing live there is simply not enough time to start mousing around. With the keyboard you have labeled, usually lighted buttons, which are (usually) arranged in a logical fashion.

With the keyboard, you carry one instrument around, which you can put up on a simple stand and plug in with one chord. Going the computer route, you have to carry several devices which you need to set up on two-tier stand (much bulkier and often not as sturdy), that need to be properly connected together.

Also, as some previous posts have said, a cheap laptop will likely not cut it for advanced setup - you may get away with spending $1000, but you will end up with a bulky setup which has the functionality of a $700 keyboard, but with way more headaches.