All else being equal, broadband woofer efficiency goes up as cone area increases.
All else being equal, broadband woofer efficiency goes down as cone weight increases (which tends to happen as cone area increases).
All else being equal, broadband woofer efficiency goes up as the motor strength increases, but the low-end -3 dB point moves higher, and the low end sounds "leaner".
All else being equal, low end efficiency goes up as the woofer's free-air resonant frequency goes up, but again we lose low-end extension.
So, like everything else in speaker design, efficiency is a juggling of tradeoffs. And the rear-world picture is more far complicated than I've portrayed it here; for starters, changing one parameter inevitably changes others, so "all else" is never equal.