All SS amps should show measurable increase as impedance is dropped. Theoretically, they should all "double down" in power output as impedance is halved i.e. 50 wpc @ 8, 100 wpc @ 4 and 200 wpc @ 2, etc.... Even though many "hi-end" amps are rated this way, reality shows that this is not the case in most situations though. One really needs to check the power at the point of clipping into the various impedances to see how "beefy" an amp really is and not just look at published specs. The less that power increases as impedance is dropped, the more that the power supply and output devices have become choked. If a stereo amp of SS design can't deal with one pair of "normal" speakers ( non esoteric design ) and drive them to "reasonable" listening levels in an average sized room, it should be disposed of. This is true whether the speakers are rated for 4, 6 or 8 ohms.
All tube amps with output transformers should remain relatively constant due to the loading mechanism known as the output transformer. While you will see some differences ( possibly in both power output AND frequency response ) when changing taps with various impedances and speaker loads, the main reason for having the output transformer is to help the amp remain consistent in performance regardless of the load that it sees. Some designs come a lot closer than others do in this respect.
Output Transformerless ( OTL ) tube amps will typically produce less power as impedance is reduced. There are probably some exceptions to this generalization though, but for the most part, i would consider it true. This has to do with the output impedance of the amp and the inability of most tubes and their associated power supplies to supply large amounts of current. As such, these designs would normally prefer to see a speaker with a relatively benign load that maintained a somewhat higher nominal impedance. They do have the potential for more pleasant sonics ( in my opinion ) as you have removed a major source of signal degradation from between the output devices and the speaker. Sean