Most usually not from a power perspective, and there's a lot of misunderstandings going around. Watts are voltage × current, and some headphones need proportionally more of one or the other. That's one of the reasons why it is generally good to leave some headroom when specing a setup just based on wattage. Then some people take this argument way too far and draw the wrong conclusions.

Depending on who you ask, and there are credible people on both sides of the argument, some headphones may sound nicer on certain amps. But then we get into the weeds of equipment that don't claim full transparency to the source and do introduce colourations. Also, you might need to consider the question of whether or not it's good to listen to recordings using equipment more perfect than what it was originally made with. Yadda yadda... We can go on forever.

Fundamentally, if your idea of listening is to replicate the source file as accurately as possible (according to current standards of analysis), then a THX amp is all you'll need for everything apart from the most ridiculously demanding headphones.