Short answer: Don't sweat it. In most cases, the choice of padding method doesn't matter.
Longer answer: why it doesn't matter. As long as you use proper crypto design practices -- in particular, as long as ciphertexts are properly authenticated -- I'm not aware of any way that the choice of padding affects security (with one exception, see below).
It's true that if you fail to authenticate the ciphertexts, then there can be attacks, as @Thomas explains. Then again, if ciphertexts are not properly authenticated, you've probably got a host of other problems, so you shouldn't blame this on the padding scheme. Cryptographers know that if you encrypt something, you really should be authenticating the ciphertext; failure to do so is a classic rookie mistake that can open up serious security flaws.
In short, if you're following good crypto practices, the choice of padding shouldn't matter much for security (and if you're not following good crypto practices, you may have bigger problems).
The exception: a case where it does matter. OK, now we're down to the fine print. This is where I admit that the above is a bit of an oversimplification. There is one situation where the choice of padding may be very important to security: resistance to traffic analysis.
Encryption does not conceal the length of the messages being encrypted: the encrypted message typically reveals the length (or approximate length) of the message that was encrypted. In some contexts, this can be highly problematic. For instance, there are contexts where revealing length information gives away the entire store: it reveals the stuff you were trying to keep confidential. (See, e.g., Chen et al's astonishing side channel attacks on SSL-encrypted web applications. Among other things, they showed that an eavesdropper who observes the lengths of network packets while the user is typing in a web search query can infer what the search query was. I think Google fixed the problem, but it was a stunning, eye-opening example of a general risk that was previously known.)
If you are in a context where message lengths reveal sensitive information, then you have a problem. The standard defense is to pad the messages before encryption, so that the ciphertext length does not reveal anything about the message lengths. One way to do this is to pad all messages out to a fixed length, before encrypting. Another (less secure) way to do it is to add padding of a random length, with enough random padding that the random noise obscures the signal and prevents an attacker from learning enough information about lengths to do any harm. So, in a context where we need to prevent traffic analysis, the design of the padding scheme becomes critical, and standard padding schemes are probably not going to be enough: you may have to do something special.
