The 12AT7 has more gain and will sound louder. Great if you want to beef up output from a DAC or preamp that normally uses 12AU7 tubes.
Because the current draw of a 12AT7 is similar to the 12AU7, in most applications a 12AT7 it can be substituted for a 12AU7 and the primary considerations are more gain (louder sound) and the perceived quality of the sound.
I used a 12AT7 in my Audio Note CD player in place of a 12AU7 and got wonderful sound from a particular Mullard that exceeded other 12AU7s that I had tried.
However, you cannot substitute a 12AX7 for either because of a huge difference in current.