What actually determines volume power? Is it watts?

OP:

Lets simplify.  If you feel you are "almost there" with your current amp and you are looking for a reason to upgrade, go ahead.  However if you feel there's a big gap between how loud you can play and how loud you want to play the math isn't in favor of a 2x power difference being your solution.

It's also possible your amp has plenty of juice but it's your speakers which are compressing and reaching their thermal and/or mechanical limits.  They do have limits. 

So, if you feel you have a big gap between where you are and where you want to go, it's more likely to be solved by higher efficiency speakers.

Have fun shopping!

Erik

So what spec do I look at instead of wattage?

Depends on your speakers.

What are you playing?

The issue may be the speaker / amp matching and knowing your speakers would help.  Your speakers may be out of dynamic range or they may have a difficult impedance profile. 

Assuming you had easy to drive speakers, and they were not even a little stressed, then Wattage would help you understand how much more you needed.  Doubling of power = 3 dB SPL.  Doubling perceived volume = 10x the power, and 10 dB louder.

Agree that we need to know the speaker.  In addition to amplifier power, speakers for the consumer market may start to compress early on.  That is, the power output is no longer proportional to input due to physical limitations of the device, including thermal.

If you double the power, and go from 1 W to 2W you should see +3 DB across all frequencies, but most speakers quickly start to compress, and produce less than 3dB gain per doubling of power. 

If you are at home, and 100W is not enough, you should evaluate the amp+speakers and even the room before making a fix, but jumping in amplifier size is not likely your answer.

@immatthewj Really depends on zooming in on what the OP is hearing when he feels he's run out of juice. 

Generally speaking, a current constrained amplifier produces a flat output into an easy load but at difficult loads the frequency response starts to track the speaker's impedance curve somewhat. 

So with an ESL, an amp will lose output in the treble.  Roger Sanders of Sanders Speakers rightfully points out you need an amp with not just current, but high frequency current drive, which his Magtech amps provide.  With a speaker with a normally bad bass output like several Focals, the amp will sound soft in the mid-bass, where the speaker dips to or below 3 Ohms. 

OP:

I'm saying that you'll only get 3dB louder, which is very little, by going to 200 Watts vs. 100 Watts. 

If you are really constrained in your dynamic range due to power, you are going to need more than that big of a jump to get to happy.

To double the perceived volume you need 10x the power.

However, not all speakers have equal efficiencies, and you may not want it louder but you want more bass.  Depends on what exactly you want to accomplish.

You may be better off looking for speakers with higher rated sensitivities than you currently have, or to add a subwoofer. 

Also, if you are turning it up for detail that's often a sign your room is too reflective.