Well, the older 9.3.3 version isn't on the postgresql site anymore. Now 9.3.4 and above are, but that means a whole new and time-consuming round of testing if we migrate up. Is there any chance of putting the older 9.3.3 instance back on the yum site? Or is some major flaw with 9.3.3 that should motivate us to get off it immediately?
The PostgreSQL versioning follows X.Y.Z, where X.Y is the release, and Z is bug-fix, so you should always run the higher Z of your X.Y version, see the versioining policy at [1]. An upgrade on Z shouldn't cause incompatibility, but you should check the first paragraphs of the release notes [2].
So, that all means you should be on 9.3.6 right now.