F=mass * acceleration
and..
F=pressure * area

... and if we're talkign about the same lifting force, F, then

mass*accel = pressure*area

So you don't get one without the other.

Sorry if I'm stating the obvious.

It is pretty easy to measure the pressure and the area, and pretty darn hard to measure the mass and acceleration. So pressure is preferred in the analysis. That's all it comes down to IMO.