Beta blockers and benzodiazepines have completely different functions.
Beta blockers keep adrenaline from binding to cell receptors which lowers your chance of the 'fight or flight' syndrome. It's also used in reducing your heart rate and high blood pressure. They will not reduce any brain induced anxiety.
Benzodiazepines affect GABA receptors in your brain. They are a sedative that reduce awareness, meaning when anxiety rears up and you become hyper-vigilant, benzos reduce the interaction between those neurotransmitters. Basically, they reduce the activity of your central nervous system.
Which one is better depends on which type of anxiety you suffer from. If it's more of a hydrocortisone/norepinephrine anxiety, beta blockers are good. If its genesis is in the brain, go with benzos. Here's the rub. Doctors have different theories on which source causes anxiety.
Now, as someone that has taken both, I would say that benzos are superior to beta blockers for anxiety/panic. However, this anxiety/panic I have is not caused by public speaking. Benzos are also addictive (over time) and if you take too much, you'll become a temporary space cadet (they are potent tranquilizers). Too much beta blockers will lower your heart rate, but not have any mental effects.
If you have an anxiety problem, the benzo is probably a better choice. But I'd test it out to make sure it doesn't make you loopy.
No anxiety problems, you may wanna try the beta blocker. Test it out at an open mic or karaoke or something. Those meds are extremely safe.