Unlike the DT1350, which sound terrible (hollow and cold) un-amped, the T51p is warm-sounding, musical, not overly analytical and relatively easily-driven directly from MP3 players (though still very power-hungry, if compared to IEMs). When driven through the Centrance DACport, T51p's improvement is mainly in resolution and control, especially in its slightly loose bass; whereas the DT1350 really come alive when paired with a good amp, really one of the best sounding headphones in its class, with superb clarity, mindbogglingly deep, tight bass, and yet still forgiving for non-lossless source (like mp3s), for sheer sound quality, literally blowing the T51p out-of-the-water, in my opinion. In short, if you just want a casual headphones to go with your un-amped MP3 player, T51p is a great choice but if you are willing to invest in a good amp and like me, you prefer more analytical, controlled sound, go for the DT1350. I've both, T51p-unamped for workplace with my MP3 player and DT1350-amped for home listening from laptop.
Comfort-wise, the T51p is the clear winner, it seems to be lighter and the clamping force is less strong, plus the new ear pads are softer, I can keep them on for 2-3 hours at a time before getting uncomfortable.