The 6L80 is a great trans, I have one in my daily drive. The 700R4 is also a good trans, I have on in my 60 Impala. I'd definatelly go 700R4 for a few reasons;
They Bolt Up (no adapters etc, just use a 168 tooth flexplate and appropriate starter).
Dont require any fancy computers
They are significantly cheaper
The aftermarket parts available means they can hold bulk power without reliability issues
Tuning the 6L80 trans (yes, they also need to be tuned) if not done correctly (similar to having an incorrectly adjusted TV cable on a 700) will lead to a very short service life.
Lastly, but most importantly, I dont think anyone has developed an aftermarket computer that will control the 6L80 yet (I may be wrong). I looked into this a while back and all indications were no. This may have changed since.
I'm very happy with the 700R4, it's like driving a different car now. I have a gear for every occasion and the overall driveability has improved.
Good luck,
Cheers,
simon