Flux I guess?
The Maxwell stress is \$\sigma = \frac{B^2}{2 \mu}\$, in units of pressure (or energy density -- same thing). If you have an air gapped core with so-and-so B in it, and ~no field outside the core, then this is the force pulling the gap together. Or if you have two magnets pole to pole, then this is the pressure pushing/pulling on them (minus the pressures at the opposite ends, mind: there is a net pressure when they are unbalanced, of course).
Flux goes as \$\Phi = B A_e\$, but force also goes as \$F = \sigma A_e\$, so we can also say \$F = A_e \frac{\Phi^2}{{A_e}^2 \mu}\$ and one Ae cancels so it goes as flux squared per area.
It's like asking, "which matters more, the voltage or the charge on a capacitor?" They're both fundamental quantities to the element, and the question implies more about the ignorance* of the one asking it, than its [direct] answer reveals about the subject.

(*Not stupidity. Ignorance is good, in that it's why we ask questions. As opposed to "you can't fix stupid".)
Flux isn't usually too important, for mechanical purposes, because you can almost always wait a little longer. A solenoid might take 500us to charge up, but 5ms or more to actually move. If it's not moving fast enough, you can increase the voltage, or goose it with some pre-drive or PWM it for constant current drive (as done with stepper motors).
Or how relays are usually noticeably slower to turn off when shunted with a diode (e.g., 20 or 30ms, on a relay that's nominally rated for ~10ms opening time). Easy enough solution there, use a zener instead of a diode to clamp the flyback. Dumping the flux into a higher voltage equals less time.

Tim