FWIW, I *prefer* online. In fact, I wouldn't now bank with anyone who didn't give me online access to my bank account. But as John says, it's safer if you stay with the online version of a bricks-and-mortar organisation, because at least then there's someone you can turn to if it all goes pear-shaped.
Higher interest rate is handy. But better is the ability to check your account, pay bills and transfer money without having to go into the branch, something which for most of us used to involve a wasted lunchbreak or sometimes even time off work. And the ability to transfer money at will between accounts means that anyone can now share money between high-interest and current accounts as you're supposed to do for maximising interest. Previously that was pretty much limited to people with lots of free time (ie. either housewives or retired), because no-one else could manage regular visits to two bank branches, and even then you had to be extra careful to avoid going overdrawn.
And for my company, I've got a business account with HSBC, who uniquely have figured out that internet accounts cost them nothing on admin and therefore are passing that saving along to their customers by not charging for transactions via the internet. Everywhere else still takes a tithe on business accounts as if the world was still using paper ledgers, which is pure larceny.