One of the problems of ECB (among many other problems) is that it encrypts deterministically. This is every time you encrypt the same identifier, you get the same encrypted text. Therefore, this mode does not prevent traffic analysis. An attacker may not be able to recognize identifiers that are encrypted. However, it can still determine when and how often the same identifier is sent.
When used correctly, CBC and OFB use a new random IV for each encryption, thereby encrypting the same identifier each time. Since you also make sure that all identifiers are the same length, the result should be encrypted if the attacker cannot distinguish between repeating identifiers from non-repeating ones.
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