I want to buy one of these to make professional quality recordings, but I don't know which to go with, is there a big difference between 16 bit and 24 bit?

Yes there is a big difference, and there is a big difference in price!
The 1680 allows 16 tracks, 4 stereo FX processors, has a nice graphical screen, and some cosmetic features like XLR jacks on a couple channels.
The 880EX (current one out) has 8 tracks, 2 stereo FX, and a cheesy little screen.
They both come standard with 2gig drives that allow about 400 track mins in MT1 (high quality compressed mode). They both sound excellent in MT1 (better than minidisc I think). They both have SCSI ports allowing backup and burning your own CDs. They can both also back up to SCSI zip drives, jaz drives, HD's, etc. and to DAT using digital outs.
Now here's the crux of the biscuit... The 1680 comes without any FX processors (they run about $300 per pair) which puts a $2500 1680 at around $3100. Another inconvenience is that the 1680 uses 4 stereo pairs on faders. They can be unlinked, but still only allow realtime mixing of 12 channels at a time.
I opted for the 880ex instead. Unlike the original 880, it comes pretty much complete. Comes with FX built in, more inputs, more disk space, better screen (backlit). Plus can track 8 channels at once (though two will be digital ins) and it has no stereo fader pairs (I hate those things). It can be had for $1500 or less (check out www.riksmusic.com or www.fullcompass.com).
That extra $1500 goes a long way towards compressors, an eq, a tube mic preamp and some mics, patchbay, cabling, and all the other crap you need to make good sounding recordings. If you don't need the extra tracks, get an 880ex. You'll still be amazed at what you can do with bouncing (as everyone is so fond of pointing out, all of Sgt Pepper was recorded with 8 tracks)

Ohh yeah, one other thing. The 880EX uses 20 bit A/D converters. I believe the 1680 does as well. I've read a couple different things, some say it uses 24 bit A/D converters and others just say it has a 24 bit internal structure with 20 bit A/D converters. The older 880 by the way was 18 bit A/Ds. None of the v-studios are 16 bit.