I prefer face to face banking because I feel it's the safest choice but when you have those busy days then online banking sounds convinient and could be done from the safety of your own home. I don't really know how safe it would be banking on phone, I just don't trust that method just yet.
I don't think it really matters. Perhaps if a person gets too worried, they could could always try some sort of identity theft protection, or some other type of security. In reality, I think everyone needs identity theft protection, because there has been too many cases of it lately.
For convenience, I prefer the internet. For safety, I prefer face-face. It depends on the amount of money I'm working with. For larger sums, I go to the bank directly.