It depends on what your priorities are, and your expectations of budget. The ZX1 is significantly better built. I can imagine the F880's buttons breaking after a few years, whereas the ZX1's buttons will be serviceable for a very long time. The frame is solid, and the brass 3.5mm plug housing is bulletproof. The rubberized back plate of the ZX1 makes it infinitely easier to hold over the slippery F880.
For SQ, the ZX1 is basically an "idealized" F880 --- Sony has always maintained that stance anyway. In that vein, the ZX1 was never going to be an astronomical jump in SQ over the F880, so if you're going by overall sound quality alone, the extra price was never going to be justifiable. Let's put it this way: if you don't listen to both units carefully, you won't notice much of a difference between the two. Only when you listen carefully do you start to appreciate the improvements on the ZX1.
For me, I'm fine with my F886, because I tend not to listen critically when on the go. I reserve nitpicky listening for the desktop, and I have a capable DAC/amp for that purpose in the Concero HP. Getting the ZX1 over the F886 for me, personally, would really only be a question of ergonomics and build quality. I constantly worry about dropping my F886 because it's so slippery, but I plan on purchasing a nice case for it, so that problem will be mitigated. Thus, there's no real need for me to purchase the ZX1.
