I kinda do both...
In most cases, i do the recording onto the 788, mixing and etc on there too.
I'm just a little more adept at having 2 hands on faders, then the whole point-and-drag setup most software has (and i can't shell out $$$ for a control surface just yet)
Afterwards, I mixdown 24Bit to an SGI Indigo 2 (the only computer i have capable of 24bit, without severly screwing sh!t up)
Then "master" the song. [read: chopping off the ends, fading out, encode to mp3 etc)
In reality, if you look at actual costs, i think the 788 will probably end up being cheaper...
Considering PC's are quite cheap, you'd need a decent soundcard, and the software... freeware [both real and pirated] aside, sequencing/tracking software is a little pricey.
Really it's up to you tho. I get along fine with my 788, but sometimes I do wish I had a "real" DAW to work with