BL over displacement is important - that is only shown as a curveCompliance over displacement is also important - show an a curve
inductance can be important - this can also be shown as a curve but its a high order derivative so its non linear effects do not directly affect the system as greatly as say compliance or BL which are direct forces on the system.
Other motor distortions such as flux modulation or unwanted eddy currents- non-conductive formers, shorting rings, motor saturation etc can deal with these
sensitivity is a big one let me repeat: BIG ONE, but you also need to consider sensitivity over the displacement which is basically xmax (give or take)
BL gives you sensitivity and resistance (or the DC resistance ace of the voice coil ) will reduce your sensitivity which is why the formula is BL^2/Re for pure motor force factor spec'ed in Newtons squared per Joule per Second, or watt. Combine that with the moving mass and cone area and you define raw SPL.
RMS is not a woofer spec its an amp spec. LOTS of brands will hype up "cooling" or high RMS - i have yet to see any conclusive results of any of it. If it helps its only going to help for very long term thermal abilities. Any and all woofers will takes tons of power short term. Which is why some brands spec SPL woofers at say 20,000 watts which for a 1 second burp is actually not impressive from a thermal standpoint, especially at a high frequency where the mechanical displacement limits wont be reached. The issues with say 20,000 watts (for example) is that the accelerations are very extreme but we don't see thermal break down over a short period of time, but you'll often see mechanical break down from high force - broken cones are very common.
The last specs are the hidden specs - durability, longevity. etc - is it generally going to last for the time i expect it to last? One major one for example is foam vs rubber surround. Foam may give you say ~1.5dB Extra SPL but it not UV or water proof and can wear away over the years. Point is here they are always trade offs to consider.
I also believe "SQL" simply stands for sound quality + loud? where SQ is stickily "Sound quality" and "SPL" is for spl woofers.
I actually think those terms are rather idiotic and misleading. In fact a good woofer can indeed be loud and sound very good. Many of this things that make a woofer sound bad also make it less loud.