What come material you would NOT buy/want? And why?
Ummm...
Paper for an outdoor Speaker?
As has been said, the factors determining choice of Driver only come down to material options in certain situations where a manufacturer may offer one motor structure with 2 or 3 different cone materials. Usually where this may happen you will be able to see the result in a sample FR graph. Differences may be in how well the cone performs at lower frequencies vs where the Cone Break Up occurs and how significant the Break Up is.
The best description I can think of is in Subwoofers, for example, where a Paper Cone can be fine, however if it is too lightweight (low Mms) it will not perform as well at lower frequencies as one may want, but the tradeoff becomes how the Cone will behave at higher frequencies... Something stiffer and potentially heavier will do far better down low, but not deliver up high as well.
In a situation like this, you have to weigh the pros and cons of Motor design and strength against cone material and how you will use the finished design in your system. If you have a Speaker that rolls off at 100Hz, say, and you want to pair it with a 18" Harbottle Driver with a High Mms that wants to be done at about 70Hz, you are making a bad design choice. This doesn't even take into consideration what material may be used because the material isn't important here!
In this example, you would be better off choosing a Driver that can perform well at higher frequencies to pair properly with the "proposed" existing Speaker rolling off at 100Hz. The tradeoff may be in LF performance for the Driver, or getting a 21" instead of an 18" as his 21" Drivers perform at a higher frequency than the 18s.
This doesn't imply that one driver is better than the other.
It is a matter of usage.
If you want a Tweeter that can perform well at higher frequencies, a Be Dome is stiffer than an Al Dome. Does that mean Be is better than Al? No. But how you are going to use it is the key. In this manner, you could also ask whether a Raal vs a high end AMT is better. Or a 3/4" Dome instead of a 1" or larger Dome.
Consider how many JBL Speakers use their Poly-Plas cones. On one hand you may not like the look or think you won't like the sound, but how many folk rave in general about the performance of some of these Speakers.
Again: It is use-case specific.
Phrased another way, the cone material is like your pants. Denim can be fine, but sometimes you want a light weight twill, and other times you may want leather. You are the same Motor, and the "cone" material will have an impact on how you perform in a manner of speaking. Leathers on a Hot Summer day is like asking a 21" Subwoofer Driver with high MMS to perform up to 200Hz.
Now, let me counter your question:
Are you asking because of true functional performance or because you want a certain aesthetic?
Designing a Speaker based on how the Drivers look vs how they perform is a bad way to go about it.
