Wattage is not just about more volume. Wattage is about energy control. High power amps can manage energy distribution and absorption much better than low power amps. People tend to believe that an amp's power rating has nothing to do with performance. It doesn't have everything to do with sound quality, but it is a contributor and that cannot be ignored.
How much power becomes a contributor to sound quality is mainly dependent on the speakers being used. For example, some efficient speakers have a high dynamic range and can absorb a substantial amount of power. They will play well with single digit-watt amps but will really shine when submitted to a matching amp that can deliver power with authority and precision. Power is mainly about speaker control and dynamic range reproduction, not simply wholesale loudness. Low efficiency speakers naturally always perform better with high power amps. I hear reports of small amps driving them well from time to time. I cannot sell an amp and say, "Well- it will work good if you don't turn it up much." I match speakers & amps by performance relative to high impact listening sessions and never low impact ones.
I have a tendency to suggest high power amps to people even with high efficiency speakers. It is a wive's tale that high power amps have to sound worse than low powered ones. The stereotype is born from this fact: It is easier to build low powered amps than it is to build high power amps. If a high powered amp is not designed right, it will sound worse than a lowered powered high quality model. There are many wive's tales out there- and the debunking thread is a good place for that.
BTW: There is a thread about power in this circle.
What you are experiencing is typical of tube vs ss amp comparisons. The tube amp is good at imaging and details while the SS one has more bass ability. Perhaps neither model is what you want? It sounds like the chasm in performance between the two is too deep to ever be totally satisfied with either one.
Note: You have to choose a model that gets both the qualities you desire in one package. There is no reason to compromise so much. A good amp, tube or solid state or hybrid can get it all right. Those two models, while probably good amps, just don't fit your requirements.