To any members who discover a website that says it has a jailbreak for iOS 6.1.3, there is no such thing. There is not and will never be a jailbreak for iOS 6.1.3. Any real jailbreak news for any version of iOS 6 will be added to the first post in this thread. Please do not post links to any sites purporting to offer such a jailbreak. Any such post is subject to deletion.
Same for 6.1.4. Note that 6.1.4 is iPhone 5 only, and I've seen a few sites offering 6.1.4 jailbreaks for the iPad Mini.... Your best source of info would be on iPad/iPhone Forums, the real Twitter accounts, as well as their respective sites. If it's not a reputable source, always second guess it