The magnet(s) are only one portion of the motor assembly, thus they are only one portion of th over-all performance of the driver. Imagine the magnet like your engine's pistons... you could say my buddy's car has bigger pistons, why is my car faster? Because there are more variables to account for.
Magnet force is only one portion of the motor's function, and the size of the magnets is only one aspect of deriving magnet force (Bl). Just as piston size is only one aspect of the engine's displacement and power potential.
Power handling comes in two forms, mechanical and thermal. Usually advertised manufacturer specs are thermal limits, because mechanical limits are so greatly determined by the enclosure size/type. Mechanical limits are how far the cone can move before things start going wrong... suspension bottoming out, voice coil bumping the backplate, etc. The larger the box, the easier this is to do.
So since the manufacturer has no way of knowing exactly which box you will be putting their speaker in, they give you the thermal limits of the speaker, which does not vary install to install as much as mechanical limits. This is how much current can pass through the coil before it melts.
Thermal power handling is generally handled not by simple magnet size, but by the size of the voice coil, shape of it, the material used in it, the speaker's cooling abilities on the coil, etc. One speaker could have huge magnets, and a tiny voice coil with poor cooling... while another sub could have much smaller magnets, but a larger coil and better cooling capabilities. And, the larger magnet does not even mean a 'stronger' motor. Magnet size, unless compared in very specific and understood terms, is all but meaningless to the average consumer. For you.... just ignore it.