Emotional response to music is one reason I spend a lot of time to compare gear. A one hour AB session is good enough to identify some differences, but weeks would be better in order to be certain about most differences.
The emotional response to music can take time to take effect, whether it is excitement, sheer joy, relaxation, feeling laid-back, etc. Other factors such as time of day, whether I'm hungry or tired, mood, and stress level can also affect the way the music is perceived. Reaching a point when a headphone and the physical world "disappears" leaving only music is an emotional experience that takes time to occur.
Some differences such as bass impact, treble extension, details, timbral accuracy and tonal balance can be identified quickly, with quick AB swaps. Other differences such as texture, soundstage, imaging, dynamics, PRaT and overall emotional response may require more time to identify. For example, one minute may be enough to identify how realistic a saxophone or drums sound, but it may not be enough to know how pleasant it sounds. Emotional response is especially tricky to identify; it can vary with the type of music I'm in the mood for and takes time to become familiar with. This requires a lot of time to become familiar with an amp and how it performs with different sources and headphones.
I agree with the points made above regarding a good source. A better source should allow amp differences to become more apparent. However, source+amp synergy can also play a part and trying multiple sources with two amps can be illuminating in other ways.
For example, suppose Amp A is relatively neutral and on the cool side. Amp B is warm, lush and relatively slow and sluggish. Paired with an accurate and neutral source, a fast and colder headphone such as the SA5000 might sound better with Amp B. Change to a non-OS DAC with a warm and full sound and Amp A might sound better with the SA5000.