Faced with the same choice several years ago, I bought the 3800. It is a much smaller unit, and fits on my desk. It handles cut sheets only, while the 4880 handles rolls, but I have not found the cost difference between sheets and rolls to be a problem. The 3800 will print on cards and smaller cut sheets down to 4x6 inches, so I can print 5x7 card stock, which the 4880 can't do.
The largest paper I have used is the 17x25 inch from inkjetart.com. It makes a nice 16x24 inch finished print. If you need to print larger than that, the roll handling ability of the 4880 might be useful. (Of course if you need much larger prints, then a 24 inch printer is indicated.)