You are on Audiosciencereview, yet you're asking about different sounding DACs?!
A DAC is not supposed to alter the sound in any way, ever!
Even 0.50ç DACs manage that these days.
Once your DAC is audibly transparent, there's no reason in searching for another DAC. They simply don't have a "sound".
Even Headphone amps don't make any difference, unless they alter the signal (e.g. tubes, NOS, too high output impedance, etc.) or cannot provide enough power to reach the desired volume without clipping/distorting.