In this case none of the existing jailbreak tools will work. Whether or not an older jailbreak method/tool will work is based on (1) what exploit was used within the iOS release to enable the jailbreak, and (2) what did Apple change in subsequent releases of iOS that could close that "hole" in the iOS.
Originally Posted by cobra302
In the case of iOS 4.3.1, 4.3.2 and 4.3.3, there was an exploit in the pdf viewer that allowed the jailbreak development groups their entry point - and the subsequent releases (4.3.2 and 4.3.3) did not address that exploit - so the existing jailbreak tools continued to work.
When Apple released 4.3.4 (4.2.9 for VZW) they closed that pdf exploit, making the existing jailbreak tools/methods obsolete, so if you have upgraded, you must wait. BTW, Apple also has to "sign" an iOS install to validate and activate your device. Typically when they release a new version of iOS, they stop "signing" the previous versions - which prevents you from being able to simply load an older version of iOS to continue jailbreaking (or to "go back" after upgrading). They have already stopped signing releases prior to 4.3.4 (4.2.9 in VZW) which is why once you upgrade, you can't go back.
BTW, the PwnageTools team released a tethered jailbreak for the new iOS last night - about 12 hours after Apple released the update... untethered jailbreak may take a while, but the hackers have already found an exploit...