I disagree with most of the above negatives..
With my band, not only do I use a laptop for backup but also for main performances..

The quality recorded to a laptop is fine for live..Use a mixer to get the settings you need ..volumes, EQ etc.

I use Acid Pro to record and Sound Forge If I need to add effects ..

After recording I save the wave as MP3, at 192 bitrate..

Advantages over mini disk ,etc...You can read a page of tunes at a time on your explorer view..and just click on a named song...I use Winamp as a player..The combination is unbeatable..

Go for the laptop..
I'll bet you will soon depend on the laptop for primary use and not just a backup..