How Much Difference Does a More Powerful Amp Make?

Approaching your question from the speaker side.
Sensitivity is not the end of the amp/speaker problem. 'goodness' of load is more about phase angle then just sensitivity. A very highly reactive load will be worse, even if much more 'sensitive'.

From the amp side. IF....you were driving just a resistor, the more powerful amp would indeed be slightly louder. Not even 3db, which would hardly be worth it. But, the load you are driving is not a resistor so as it turns out, amps vary in ability to drive such non-resistive loads. It is just possible that the lower power amp will be a better electrical match for your current or proposed speakers.

For the above reasons, 'hi-current' amps may be a red herring non-spec. Since speakers are not a resistor, the real measure of an amp is how well it does into a real load. Which the published specs don't help with.

As for 'real world' performance? Read Kijanki post above. 10x power=2x loudness. Not much for such a huge increase in power. If all speakers were of the sensitivity they advertised, much better leverage could be gotten with more sensitive speakers than the amount of amp power you are talking about.

Check out this link for real-world amplifier testing.

http://www.sonicdesign.se/amptest.htm

IMHO, and perhaps more so with ss amps, having some extra power beyond actual use, is worthwhile in that it can keep an amp from stressing near it's clipping point.

I had a Classe CA 300 on a pair of PMC MB2 once and turned the amp up to its limit and then put on a Classe CA 400(only 100w more But 1kv bigger transformer)and that made a huge difference when pushing a great song up into the bigger SPL's.
I have had a Simaudio Titan(200w/ch) and it would hold its own..
The $$ value vs power may not be worth it...maybe W7M's

The C.J. LP280 used a more complex circuit than the LP140 or 70 .

A better amp is more important than a more powerful amp. Don't be mislead by the numbers game.