When we talk about secure passwords (Not PINs for the moment, I'll get back to those in a moment), we're mostly worrying about how easy it is to recover someone's password from a database once a system has been compromised. However these days, we don't store the password, we store a hash of the password. To recover the password, the hacker has to successfully 'un-hash' the hashed password, which is done by applying a brute force cryptographic algorithm. The computer detects hits by examining the frequency of letters in the output, knowing that letters don't have an even distribution in passwords (or any other text). Choosing a random password is actually useful in this case, because even if the computer correctly finds the right key for de-hashing, it doesn't recognize your password as 'de-hashed' and just passes right over it.
So, for passwords, it is fairly clear that a random password is going to be safer than a word / name or other commonly used password constructs, in its ability to resist extraction from a compromised database.
Can we make the same claim for PIN codes? It would be harder - you only have 4 digits to work with, which makes it much harder to determine if digits are distributed in a pattern or randomly. You would expect a lot of false positives and false negatives. Nevertheless, distributions in real life numbers do exist - http://en.wikipedia.org/wiki/Benford%27s_law is an obvious example, which leads us to the non-obvious conclusion that making PIN codes longer probably leads to a lower level of security. On the other hand, the scenario in which this is a problem is when a database is compromised, and bank databases are amongst the most hardened targets on the planet, so the increase in risk is probably negligeable.