Allentown, PA area on AT&T. iPhone 6 with recent 8.4 update. Siri and dictation no longer connecting on data but functioning on wifi. Attempted to fix with reboot, moved ahead with network settings reset, hard reset, restore, and finally erase and start as new phone - all failed to fix. I used diagnostics through support and was told to bring phone in. I am glad that I found this thread before heading in this weekend. Since reading, I tested the phones on 8.3, and all are having the same issue.
One thing to note: our data usage spiked in the past two or three months. Our phones were using a considerable amount of data while connected to wifi. We made a complaint to AT&T last month. Unfortunately, there was a language barrier with support. I ended up disconnecting without a solution but received a refund for the added 3GB (which was used in three days!). Perhaps the current network problem is somehow related to an attempted fix. Check on your usage with AT&T. We have five iPhones on our account, and I only checked for usage during increments when I knew all five phones were on wifi. It was not uncommon for 80+mb chunks of data used per phone. We disabled all apps with data access and still had the issues...