I completely prefer Dyna Cabs.
I had such trouble getting great tones from static IRs for so long, but I knew others got great tones from them, so recently I started going deep into static IRs as a challenge to my own tone creation. It was just something I had to do for my own sense of accomplishment.
But still, to me nothing beats Dyna Cabs. It's those in between spots that might be just perfect for a particular tone. Not to mention, if you set the mic position, tweak the amp, and the tone still isn't right, you can then easily nudge mic a hair to get it just perfect.
And of course, for workflow, it beats all movable mic plugins, because you don't have to interrupt the creative process to create a static IR from the plugin, import it through Axe-Edit, then select it through the cab block; you just nudge the mic and you're right there!
On top of that, you've got the ability to trim your movable IR as you're tweaking, even to smooth it! I mean, that's totally ideal, and the DynaCab feature in the hardware is the only movable mic software that does that, as far as I know.
And for me the other big advantage: the auto linking of speaker impedance curves! I went for so long too broke to buy the amps I wanted, I'm making up for it now in the virtual world of the Axe-FX III, so I'm always trying to recreate the real world experience as closely as possible. This does it.
There are still great reasons to use static IRs or the movable mic plugins though, like getting off axis tones, maintaining the natural phase relationship between multiple mics, etc.
I've wondered if something with a ton more internal memory, an Axe-FX IV, might have Cab Lab levels of movable mic storage built in, with the ability to import more, but that will be interesting to see.