If you want to hear an amplifier sound "different" get a tube amp with an output impedance of several ohms! Ohm's Law rules here! A frequency response that will follow the varying impedance of the typical speaker.There is far more to it than that!
Distortion plays a major role in the sound of any amplifier due to how the ear/brain system treats distortion, which is to say it treats it as a tonality. We've known this fact since the 1930s (see Radioton Designer's Handbook, 3rd edition).
Most solid state amps are designed to have minimal distortion and is why so many of them sound the same, which is to say, harsh and bright especially at higher volume levels. Now tube amps actually make more distortion, but because they have lower ordered harmonics in greater percentage quantities than solid state, the ear's masking principle allows the lower orders to mask the presence of the higher orders. This is why they sound smoother. The odd bit is that the presence of the 2nd or 3rd harmonic (both of which are treated the same by the human ear) causes a greater sense of detail and soundstage definition! This is why tubes are generally more detailed and have more depth.
Now if we could eliminate distortion entirely that would be great. But we can't, so it appears that an injection of a 2nd or 3rd harmonic is beneficial to solid state designs. This is recognized by several prominent solid state designers in high end (John Curl and Nelson Pass come to mind) and it should be no surprise that they have turned out some of the more highly lauded solid state amps as a result.
It is this bit of understanding about how the human ear works that is one thing that's changed in the last 20 years and it is perhaps the most significant- parts and topology notwithstanding. Its our ability to take advantage of how the ear works through engineering that yields the most progress. We're only just now starting to crack that nut.