More volume comes from moving more air. You can move more air by: a) having a bigger surface area with which to move it, b) by being able to push harder, c) by having a speaker that translates smaller amounts of current into more movement, or some combination of the three. How well small amounts of current are translated into piston-like movement is partially associated with magnet type, but more likely associated with the size of the magnet (and especially the distance from the magnet in the gap) and the stiffness or "compliance
" of the cone and supporting structure. Remember that magnetic force is a function of distance, and if the voice coil is sitting suspended a great distance from the magnet (which is good in some ways, because it won't rub against anything and risk friction-produced heat buildup and frying) then it will take LOTS of magnetic energy to translate into voice-coil movement. Moreover, if the cone is stiff and heavy, it will take comparatively more energy to translate into the same amount of air movement. That particular aspect is not a function of either magnet type or magnet size. You can have small ceramic magnet structures with extremely efficient transduction, and large alnico or even neodymium magnets with inefficient transduction. What you look for is a generally more efficient speaker of whatever size you need.
I poked around for a compact definition of speaker efficiency and stumbled across this: "Although a speaker's efficiency rating is almost always correlated to its sensitivity rating, it is actually a different measurement. The efficiency rating for a speaker is a measure of how well a speaker converts watts of electrical power into watts of acoustical power. Most speakers have a very low efficiency rating — between 1% and 10% — so manufacturers rarely provide this information, choosing instead to list sensitivity ratings.
"Sensitivity' is generally rated in terms of decibels at a given distance with a given power level input. For instance, the Jensen P8R, with an 8" cone, a 200gr magnet, puts out 92.5db at 1 metre with 1W. The P10R, with a 10" cone, and 200gr magnet, produces 95db at 1 metre with 1watt power applied. The C12R (a much bigger speaker) has a 270gr magnet yet produces 93.8db at the same distance with the same power applied. The Jensen Neo-10-100 is also a 10" speaker with a 200gr magnet, yet produces a 98.9db output level at 1 mitre distance with 1W applied.
Obviously more efficient. So, it is somewhat possible to have a sense of potential loudness from specs.
The sensitivity is not the only factor, however. A speaker pushes backwards and forwards. Backwards and forwards air movement can often cancel each other, reducing audible output. Here, cabinet properties can make a substantial difference in how loud the speaker sounds, by virtue of how effectively it can move air (without cancellations) in those parts of the spectrum where the brunt of the signal lives. That very same Neo 10 speaker will be substantially quieter than the Jensen P8R if the P8R is in a properly designed cabinet and the Neo10 is merely suspended from a coat hanger.
Related to this is the subjective loudness of a speaker. Keep in mind that the human ear is not a flat audio transducer. Some frequencies enjoy greater transduction efficiency in the ear than others. If a speaker has noticeable resonances in those areas of human hearing where we are more sensitive, it can *seem* louder and cut through better.
Note, finally, that with great power comes great responsibility. Big speakers that are supposed to be able to handle large amplifier outputs tend to have heavier voice coils (thicker wire, right), and heavier cones that can remain rigid despite the pummeling When an amplifier is severely restricted in terms of power (and, having a tweed Princeton nearly identical to that Angela instruments single-ended 6V6 amp, I know whereof I speak), often a smaller-to-medium sized speaker rated at lower power (e.g., a 10" rated at 25W power handling) will be far more responsive to the types of outputs thrown at it from such an amp, than will a 15" 100W speaker. Fast n' light is what you want.
What all of this says is that:
1) You look for a speaker that shows some serious efficiency;
2) You go for a sensible power handling rating that comfortably (but not excessively) handles what you plan to throw at it;
3) You do what you can to provide the most efficient cabinet feasible;
4) You look for a speaker that "cuts"..