What does moving from a 150 watt amp to a 400 watt amp get 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. 

I have been in this game for over 40 years and spent many thousands on equipment. I even build my own speakers now. I have less than 1000.00 in my current speakers and would challenge any 5000.00 soeaker in the world for sound quality!

A lot of these responses are flat-out wrong and / or confusing! Yes, your speakers WILL sound better with a 400 watt amp (asumming equal quality), If someone thinks higher amp power is just about maximizing volume, they are clueless about music reproduction. It is more about the dynamics of the sound throughout the volume rang. Your speakers will sound more dynamic from lowest to highest volume.

This means bass will sound tighter, treble will be more distinct, mid range will be slightly clearer but not necessarily more detailed or musical. That depends on the quality.

I would would not sell your amp and get a lower quality amp with more power. In that case you would be trading musicality for dynamics. That is the challenge in musical reproduction, combining musicality with dynamics. The only way to do that is spend more money!