Yes, a full face helmet would give more protection. i slipped off a motorbike one on a roundabout. I went face first into the kerb and ended up with a stiff neck and a scratch on my visor. I wore open helmets occasionally before that.
I must admit, I'm not convinced by the design of cycle helmets, which is why mine's a snowboarding one. I wear it most of the time, but not when i go shopping or somewhere where carrying it would be inconvenient.
I don't advocate compulsory helmets, but I would advise people to wear one. It doesn't matter how safe you ride, You can't really plan for the guy hitting you from behind while texting, in which case the back of your head is likely to strike the windscreen pretty hard, or, as happened to me, a twig got thrown up by the front wheel. It jammed between the mudguard and tyre, which locked the wheel instantly and sent me straight over the handlebars into some nettles. It could have been a tree anywhere else. Some people are lucky, they win the lottery. Others are unlucky and get wiped out in freak accidents. You can't plan for everything, so you have to find your own balance of protection and risk.