I can probably answer your question directly as I own the JBL 590 and JBL 4367. I have played them back to back in the same room.
I agree with Phusis and would add it is all about “power to weight” of the system. Speakers are a mechanical system and it is all about power transfer… nothing more. There are a number of things that affect it.
big drivers that don’t move much or lots of smaller drivers that work together to not move much (line source, live venues). then there are horn and driver shading (line sources) that increase directivity which also can make things more dynamic.
It is important to talk about the same thing. What are dynamics to you? Is there a specific frequency you listen for? For me it is most notable in the drums. Does the leading edge “hit”, does the snare snap? Also low bass can greatly affect our perception of dynamics. That 50hz bass drum is critical. Maybe the seal speaker loads your room in the bass better/different.
anyway the 4367 is the most dynamic speaker I have ever heard/owned. I am often shocked at older music of my youth (Grunge/80s metal) which seemed totally dull from a recording standpoint now has some punch/snap to it. Audiophile stuff is easy and sound great as expected. I am not sure how much of that is found in the 4349 as I have not heard them. There is a bit of magic to getting the compression driver crossed over as low as possible and the 4349 is still pretty high as 1500hz. Where the 4367 is at 700ish. That to me is the biggest difference between the two speakers.
I need to listen to the 590s again to comment on them directly regarding dynamics. I was more interested in comparing detail and frequency response. If you want my opinion on the 590 vs 4367 for dynamics just let me know and I can listen again. The 590s are my rear speakers so not a big deal to move them.