There are a few, but the one in particular is E Project on youtube.Could you perhaps link to the comparison you are referencing?
Assuming there is no overload/clipping/very excessive distortion on either device, the usual suspect when a difference is heard between electronics is level matching, or specifically whether it is precise enough. It is said that as little as 0,1-0,2 dB level difference can sometime skew listening tests.
Apart from that, some amplifiers have large output impedance, which can indeed cause significant deviations in their frequency response when driving a real (complex) load like a loudspeaker, and this could of course be audible. Maybe the explanation from this post and this post will be helpful. These deviations are typically less than 1dB and can be removed with EQ.
However, even relatively cheap amps (e.g. have a look at Hypex, ICEPower or Infineon...) today can have very low output impedance, which means their frequency response will be completely unaffected by the load - in which case they should sound the same as other amps with low output impedance.
Thanks for the explanation. Definitely not opposed to going the inexpensive route.
You listed chips inside the amp, right?