You mention two separate issues but intertwine them: presence of midrange/associated warmth, AND pace/rhythm. These are two distinctly different aspects of reproduced sound that I think need to be addressed separately.
Pace and rhythm - what makes you tap your toe has more to do with an amp's synergistic relationship with a speaker (load, cones, etc.). Some amps are faster than others, and this can lend a better sense of timing. Some amps have a greater damping factor, this will allow the amp to “grip” the drivers – starting and stopping them authoritatively. I'd suggest that what you like in the JBL's is your amp's ability to better move the drivers than with your Shearwaters.
Warm mids/bass, but less accurate:
One might be correct in assuming that the drivers and crossover components in the JBL roll-off the frequencies at the upper and lower regions of the spectrum. This would place particular emphasis on the midrange frequencies, and thus more presence. The JBL crossover might also be of simple design (by lack of need) - this can also improve sound.
So… your JBL’s boogie while your Shearwaters waltz…
One might consider the speaker motor/materials used to fabricate the speaker/surrounds. I would suspect that the JBL surrounds are more flexible than those on the Shearwaters. I also suspect that the JBL’s design is less damped. So… right there one could surmise that the JBL’s would require less energy to move/control. It could also be assumed that while making the driver more efficient to move this flexibility might also make the driver less precise in its excursion (and therefore less accurate). This would also produce a somewhat warmer sound. …AND would also explain (to some degree) your perception of greater rhythm or pace. …A stiffer surround material and more heavily motored/damped design would require greater energy to move as quickly as lighter-motored/coned/damped & more flexible surround design. A STRONGER and FASTER amp would bridge the gap and lend greater control.
As with most things there are exceptions to every general rule. …But synergy is the key.
