What does moving from a 150 watt amp to a 400 watt amp get you?

Invite a 170 pound 60 year old to hit you like a football tackle. Then invite a 260 pound college football player to hit you like a football tackle. Take the data generated and apply tangentially to amps.  

Glad I could clarity that for you.  ;)  

It's all about sensitivity and headroom. If your speakers make 90db with one watt. Then they will use one watt no mater if you have a 50 watt or 500 watts amp connected to them . The only difference is you paid a lot for those extra 499 watts that your not using. You need headroom for the loud spikes especially in classical music but 15db should be more than enough. So to get that headroom you need your amp will need  to deliver 16watts. Quality watts are expensive.  Doubling an amps power often means a doubling any of its problems plus a quadrupling of the price. If you don't need them then it's better to go with a lower powered amp with higher quality watts.

“What does moving from a 150 watt amp to a 400 watt amp get you?”

250 watts yuck yuck!

sorry, just couldn’t resist!!

POWER !   I had not heard my DQ 10s, not really - until I went from a 60w/ch tube amp to a 250w/ch ss amp.  It then rocked out! drums were heard AND felt, bass lines became distinct, dynamics went through the roof.  It became capable of inducing FEAR also when in a film we were watching had some low, threatening sounds played.  

Let none tell you it doesn't matter, my friend. 

@douglas_schroeder Your analogy fails because you changed 2 parameters with the assumption the new amp had a different (better?) quality. Reverse the terms such that the older man is heavier and see if it still holds true.