For every frequency, headphones have slightly different impedance and sensitivity (power needed to product a certain volume). In principle if an amp is underpowered the headphones can sound loud enough but the frequency response is distorted, particularly towards the extremes, because the amp can’t power those frequencies. This is why people say the bass and treble are lacking.

Very generally, I’ve found that if a pair of headphone produces “listenable volumes” but are not actually loud when the phone volume is at max, then they’ll perform better with a more powerful amp.