I bought a P800 last month when my old 3880 had stopped printing either PK or MK. I did the best I could to try and fix it but it just did not work and after throwing $200 down the drain in wasted ink on cleaning, I decided to quit.
The good thing about buying a new printer is that you get a full set of ink carts, which in itself is a $500 value. You do lose about a third of that in priming the lines but there is still enough left over.
The printer is a bit easier to set up and has a better interface, allowing you to set various parameters. All the newer bits are covered in the reviews.
From a user's perspective, it does print beautifully, I just did a batch of 13X19 on Moab Slickrock Silver (which, IMHO is the best metallic paper around) and they are superb. I can't say if the overall quality is better than the 3880, the print speed does seem faster - no formal testing though.
I agree, fine-art prints are a pain to feed through, sometimes it does take several tries, but I don't do them that often. The regular tray and paper-feeding path is improved, because in my old 3880 if I placed more than 2-3 large size papers of heavy stock, it would not feed, with the new one, I can put 10-15 heavy, large papers and there is no problem.
My favorite papers for the P800 are:
Moab Slickrock Silver for high gloss, high micro-contrast images
Canson Infinity Baryta or Ilford Galerie Gold silk - they are both identical papers but the Ilford profile is better. Canson's profile is too yellow. Fortunately you can apply the Ilford one for Canson paper and it works out great.
Epson Exhibition Fiber: Very nice too, but I think the Baryta is a bit brighter.
Still trying out others. Hahnemuhle Pearl works a bit better than it did on my 3880, but I think this is still a paper looking for the right printer.