Defining your use of "better" would help, but working with the general use of the word here is what I find in a good amp.
1.) Low harmonic distortion ( THD < .002 % )
This gives a nice clean signal without distorting the input waveform
2.) High signal to noise ratio ( SNR > 98dB )
This allows the noise floor to be low enough to prevent distortion and other adverse effects )
3.) Larger frequency response ( FR: 10Hz - 30kHz )
At minimum you want to include the entire human audible spectrum which is typically 20Hz - 20kHz, but I find the wider the FR is the better.
4.) Lower output impedance ( X < 5 Ohms )
Anything else higher can lead to, call it atypical, frequency response issues along with distortion
5.) Output power at 1Khz ( P > 250mW )
This is something I look at to make sure the amp can adequately drive the many types of headphones out there. Due to headphones having not only different impedances, but sensitivities as well, the higher the output power up to 1W the better. Any higher is just ridiculous and too much power for most practical use headphones.
Those are the 5 things I look for in the specs in determining a better amp. The next thing I do is check the physical design including how the power supply is implemented as well as functionality. The final test is to listen to it and compare it against what I already have.
Thanks to nick for cathing my typo.
Edited by NA Blur - 12/2/11 at 2:29pm