Power versus volume is a logarithmic scale in hi-fi. If you double the power you get 3dbs more volume. If multiply the power by 10 times you get 10 dbs louder. Multiply by power by 100 and you get 20dbs louder. If you set your speakers up in the middle of your lawn, for every doubling of the distance you sit from your speakers you get a 3db drop in volume. In a room the drop is less than this due to room echoes.
Amp and speaker maximum power ratings are a very general guide. Some manufacturers exagerate. Also some manufacturers are quoting different specifications for their power levels. EG amp power output into an 8 ohm load is the usual specification, some might quote the power into a 4 ohm load which should be higher than into 8 ohms. Also for amps and speakers you have continuous power - the power it can deliver or take as a sine wave left on all day. Or they might quote instantaneous power - the power it can deliver or take with a transient peak lasting a small fraction of a second - which will be larger than the continuous powr rating. Usually power is quoted per channel. Cheeky manufacturers might be quoting total power for the stereo pair - ie doubling the per channel rating to give a total system power rating.
I use 8 watt amps with speakers rated at 100 watts continuous. I also use 300 watt amps with speakers rated at 50 watts. They sound fine as long as I keep the volumes below space shuttle take-off levels to avoid amp clipping or the risk of damaging the speakers. Usually it's the tweeters that set the limits on power handling for speakers. The tweeters that I repaired had thinner than hair wire for the voice coil. Putting more than 50 watts through them would burn them out like an old filament light-bulb.
With amps the quality of the first watt is most important. Maybe even the quality of the first milliwatt. The first watt will be giving you volumes from 0dbs to 80dbs or more (up to 105 dbs for the most efficient speakers). 80 dbs is pretty loud. 105dbs is LOUD.
If power specifications have been measured to the same standard then watts are watts and it's complete nonsense to say that an amp sounds louder than the specifcation without clipping. What you might get is less horrible sounding clipping distortion with some amps - eg valves - than with others - solid state. The clipping distortion will still be there with both amps.