Advantages of beryllium?

Completely ignore what johnk suggests about vintage speakers. The very few Be drivers made back 40 years aren't representative of the modern state of the art. What's more, modern speakers are built and perform vastly better than the 50's, 60's, and 70's products and the measurements leave no room for debate. 
As for the safety of Be drivers, you definitely don't want to break them. Just sitting there doing their job they're completely harmless. I don't think anybody makes more Be drivers than Focal. They're very nice drivers but they take a long time to break in. I personally wouldn't hesitate to buy them. 

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.  

Paradigm's new Persona line use's Truextent Beryllium mid/bass driver's and tweeter's in the entire line. 

Don't be fooled just by the Be brand. They are not all equivalent, certainly not in frequency response or dynamic range.

In _theory_, be is very stiff and very light, so least stored energy or resonances of most materials.

The implementation of the suspension, motor, and overall speaker design is VERY important. Done well the best Be tweeters are among the best tweeters. But so are the best AMT's and ring radiators too!

Best,

E

One good eye opener, listen to the Magico Be tweeters and compare to the Focal's.

Personally I find the tuning of the Magico's a bit bright, but butter smooth and wide dispersion spanks all the Focal's and certainly the B&W diamond tweets.

It's all in that luscious motor assembly that's behind it.

Best,

E