DT1350 has much better treble extension and more controlled bass. UE6000 is much warmer sounding and easier to the ears but bass is more loose. UE6000 is much more comfortable than DT1350 and more portable as well (opinions may wary regarding the portability!).
DT1350 might sound more HIFI at first because it's brighter but I sold my DT1350 when I received my UE6000. I use UE6000 with my RockBoxed Sansa Clip+. I use meier xfeed and EQ the bass a little bit down to reduce the boominess. UE6000 sounds really satisfying with this setup.