Well...
Ultimately, there's no difference... because eventually you commit the MIDI parts to audio (to mix it to a stereo CD or MP3 or however it gets delivered).
The difference is in flexibility up to the point of finishing the mix. If you record your keyboard parts as MIDI data rather than audio, you can do all kinds of stuff with it. You can fix individual bad notes, quantize the start times of the notes to lock them in or "humanize" them to loosen them up a little, transpose sections, copy parts from one place to another, print out sheet music from it, change which instrument is playing the part, etc., etc. Tremendous flexibility. If it's recorded as audio -- well, you can cut sections out, repeat sections, even change pitches here and there (a step or two at least), but you have much less flexibility.
Not to mention the amount of disk space you can save by having MIDI tracks rather than audio tracks.
Here's an example. Say you have a keyboard part and it has a line that you want to double with a trumpet patch. If you record strictly audio, you have to play the keyboard part, then arm another track and replay the parts you want to double with the trumpet patch.
If you did it as MIDI, you could copy the phrase you want to double out of the keyboard part, paste it to another MIDI track, and assign that track to play the trumpet patch. If you don't want it to be quite so robotically precise you can vary the start times by a few ticks, edit the durations, edit the velocity (loudness) on a note-by-note basis.
(Ooops, I see Dr. Stawl snuck in there while I was running off paragraph after paragraph...)