In terms of the diaphragm, both Al and Ti have very similar stiffness with a given density. So when shaped, the weight will be quite similar between the to when targeting a specific stiffness performance, but the titanium part will thin in comparison due to its much greater density. Titanium will be somewhat more forgiving if over driven or out of bandwidth as it has greater internal dampening as compared aluminum alloys. So while Ti is a touch better than Al in overall performance, there is an added cost to its source and manufacture.
Be on the other hand can perform at much higher levels than either Al or Ti. A higher modulus than Ti and lower density than Al. This causes it to be highly damping, but not internally. Being very rigid, a Be diaphragm maintains is shape under a significantly high stress, but internal dampening is more about specific elasticity and this is where Be and Al share a commonality as neither have much elastic capability. Ti actually has quite a bit more elasticity, especially for a metal. So with Be or Al, its important to not go beyond the designed capability. Its important to do so with any driver, but the resulting output distortion will be higher. The designed capability will be very driver specific as the shape, size, thickness, quality of process will dramatically affect these figures. FEA applications will be primary point in the design process for modern drivers.
When Be is being formed, the dust that can be inhaled that can be hazardous. When formed in shape, its pretty stable and even when broken isn't quite as hazardous as it would be in a manufacture facility with volumes and processes being applied. It still needs to be handled appropriately in those situations.
