I was comparing BW for both printers before my decission. Both give outstanding results for BW prints.
I am not sure in what mode my Pro-1000 prints have been made (colour ICC or BW), but there was some color ink used when examining picture under magnification. The same stands for P800 in ABW. In both cases, color ink usage was marginal.
Perceptually, ABW mode in P800 have been improved compared to 3880 and gets closer to a look of QuadToneRip prints (in case of 3880 the difference was obvious).
I have also made some prints on P800 with ABW on matt papers, especially Hot Press and was surprised with quality improvement (what was also caused be the new black ink in P800, Pro-1000 has similar but more neutral. Epson inks are a little bit warm so more color toner is used for neutralisation. Personally I don't mind it since I do not like pure neutral look).
Epson gives you opportunity to use QTR for BW, which gives outstanding results. Canon allows for TrueBW application but I am not sure if Pro-1000 is supported and no PK/MK switch.
Finally, I have chosen P800, mostly due to QTR support, own recognised workflow for 3880, a little bit better behavior for matt papers, and possiblity to convert to Piezography inks in the future, but both are great printers.
Hope it helps.