Now that you put it that way...
My favorite classic woofers have been the light coned vintage JBLs. 2220A, K130, K145. The fact that all three are alnico may or may not have been all that important. None are great at deep bass, but they have a “liveliness” that I find very desirable. The first two have curvilinear cones and the K145 is a straight sided cone and all three have very different motor structures.
I haven't really studied the differences, but look forward to your thoughts and discoveries.