I trust TAIG way more than I do PP, who was accused of stealing the code from TAIG. You can now download TAIG 2.2.0 which supports iOS 8.4. Enjoy!
It appears that they have not updated their website as of yet. It has been updated now: Taig.com/en. They even have a Mac version now instead of Windows Only
current versions as of updating this on August 2o:
Mac: Taig 1.1.0
Windows: Taig 2.4.3
You may still want to hold off for a day or so if you can so that they can work out any bugs if there are any. Don’t be afraid to jailbreak using the TAIG tool though. If there are any bugs you will be able to quickly update via Cydia.
Update: It seams that this jailbreak works perfect for iOS 8.4. I have not had any issues with it. Hopefully with the release of iOS 9, they will release a jailbreak right away for us!