MP3, FLAC. I don't hear any difference between a well ripped 320 kbps MP3 and a FLAC, but have all the CDs I still have ripped to FLAC because it is lossless and the disk space is largely a non-issue nowadays.
I wouldn't bother with higher than CD quality FLACs, though. There is little benefit in going above the standard 16 bit / 44.1 kHz quality, except maybe if that higher bitrate also happens to be based on a better master of the recording.
As for DAPs, it probably horrifies some people here, but I find that running the HD800 from my DX90, it sounds just fine. I can't detect any sound quality difference between the DX90 headphone out and the headphone out of my NAD amplifier with built-in DAC.
I can really feel the difference between 320 Kbps Mp3's and normal FLAC's and also 24 bit Vinyl ripped FLAC of the same song.
My example would be the Beatles - Strawberry Fields Forever song - in which I can really feel quite a big chance from the different formats used to play the song. And this is coming from a guy who spent 400 euros on a CARDAS Clear cable for the HD800 and now uses the default cable because it's lighter - as there's no significant differece between them.