Since SSH keys are stored on your computer and never go over the wire, they are inherently more secure than passwords. Even if you pick a terrible passphrase for your SSH keys (or none at all), an attacker still has to get ahold of that key (barring someone patching your random number generator to return one of 2^10 numbers...)
With passwords, if everyone needs access to an account on one of your servers, then everyone has to know the same password. If one of your coworkers goes insane, you have to change the password (and probably a lot more than one) whereas with SSH keys, you just remove their key from the authorized_keys file and they're gone, nobody else has to worry about it.
Similarly, if people need access to some accounts and not others, you can segment access with keys much more easily than with passwords
Entering passwords gets old really quick. With the superb ssh-agent in use, you shouldn't ever have to do that, and as long as you remember to lock your computer when you leave it, you're as secure as if you were typing your password in every time