I have both a R1900 and a 3880. For color glossy, luster or satin prints, it is almost impossible to tell teh difference between the two. On matte paper, the 3880 is lightly better for color prints. For black adn white or monotone images, the R1900 introduces color casts that are simply bad.
If course on the R1900, you are also limited to 13" wide prints. I kept it for smaller color prints, because I need something to print CD/DVD's, and for color document printing.It also does roll printing, but mine has never handled rolls very well, waisting lots of paper.
I bought the 3880 for the 17" capability and much better monochrome capability. It makes great prints on any paper.(I use Epson, Red Rive and other papers.)