The Dalis "hit harder" and more solid in the bass, with a bit more bass depth and so a bit more size, but not a really big difference in "bass image size" so a stand up bass sounded similar sized on the Josephs. HOWEVER as we go up the frequency range, like most speakers I hear, the Joseph sonic images loose a sense of size and acoustic power, so things get smaller and smaller until drum cymbals and high end synth bleeps and blips sound more teeny.
But on the Dali speakers, while still "pear shaped," there was more size and heft maintained from bottom to top, so drum snares sounded bigger, higher woodwinds sounded more life sized, acoustic guitar strings sounded bigger, fatter, and even in electronic music, some bleepy blippy stuff I love, even the high register notes, sounded thicker, bigger, more solid and dense. So the speakers maintained an overall sense of scale and acoustic presence and power from top to bottom that just made everything sound bigger and more substantial, not just the bass parts.
I suspect that you were listening to some fine, dynamic music with a high crest factor. I have a theory that smaller systems suffer from power compression when reproducing such music, but the effect may still remain undetected as such by auditory system. It's just loses sense of scale or dynamic contrast, and vice versa (in case of a larger system). To see what I mean, take a look at this example:
This track is in fact what I would describe to be very dynamic, but the dynamic range is mostly to preserve "snaps" , "clicks" and "kicks", which are very sharp transients, just single vertical lines and mountains when zoomed in this excerpt:
The first one is the "click", followed by a single mountain peak (kick drum), and then something resembling a jagged square wave (bass guitar with modulation effects), and then again a sharp "snap", and so on and so forth. But look at the levels of the peaks! For a system to have any chance of reproducing this loudly without compression, it would have to deliver the "thump" of that kick drum basically in a single blow. Also the high frequency transients.
For a small system it would be easy to fill the room with that lovely bass guitar lines and even provide some sense of envelopment. But guitar is very much down in level and power demand than the transients, also sustained enough for a perceptible pitch. If a system is incapable of delivering the uncompressed transients in this case it would be very easy for the compression to be inaudible, right until the distortion becomes audible. But before that, it would be only sounding louder, and not any "bigger". Keep in mind that transients are too short to have any definitive pitch, they are just low and high frequency attacks of energy.
IMO, the order of things would be, as you go up in level, small system first would "flatten" the peaks, but still be able to deliver "bass guitar which is already distorted on purpose". Peaks are too short and compression remains undetected. Then you go up in level because it still doesn't sound bad and the system responds by just being louder. It's because of the distortion starting to ramp up, but still inaudible as such. No clipping indicators and no audible distortion, but still everything is sort of constricted.
I may be wrong, but it's just the way I'm contemplating on this matter.
On the other hand, at least on my system, as I go up in level, this track just keeps getting bigger and the kick drum just hits hard like a gust of energy but almost inaudible, just a discreet "thump". Higher frequency "snaps" are very life like, loud and clear. Bass guitar is visceral but not loud, basically as it should be. There are also pretty big tom attacks as well. All well sorted, with well defined imaging and not masking each other. I realize that this is highly subjective, but I don't know how else to describe it.
Here's the spectrum of this track. Quite the low end, it appears to be: