I found that both printers are identical in quality and I believe the decision is very simple, if you print from rolls on one paper type (matte or gloss) and print a lot of panos over 37" then buy the 4880, if you like borderless sheet printing, use both matte and gloss papers then buy the 3880. My friend and I just went through the same decision and we both purchased the 3880, however at the time the 4880 was about the same price. Paper handling is hit or miss it seems, I haven't had any problems with any papers even at 17 x 25, even if I cut them from a roll. Some get head strikes with Ilford Gold Fibre Silk while others like myself don't. Also, though I never validated the print speed, according to the specs the 4880 is significantly faster. If I had to do it all over again, I'd probably buy the 4880 because I'm not printing much borderless except for some 5x7 and 8x10. The 3880 runs a little quieter, however you can get 110ml or 220ml ink cartridges with the 4880, which I'm assuming are cheaper per ml than the 80ml cartridges that come with the 3880. The build quality is better on the 4880 but that doesn't affect the prints.
Less expensive (slightly)
80ml ink cartridges could be a plus or a minus
Borderless sheet printing 4x6 5x7 8x10 etc.
Not as heavy
Quieter in operation
Cheaper to switch black inks PK / MK
Better build quality
Faster print speed
110ml or 220ml ink cartridges
Vacuum paper hold down
Panos muuuuuuuuuuuuuuuch longer than 37"
With rebate can be about same cost as 3880
I just checked and with the $500.00 rebate on the 4880 they are basically the same price.