Ok. So my next guess would be to run a speedtest from both the iPhone and from the iPad using the same application. Any significant difference?

The few posts I've seen about the problematic WiFi on the iPad 3 seemed to indicate that the iPad 3 had weak signal strength when compared to other iPads in the same location. But you indicate that all devices have full signal. Maybe the SpeedTest will show something? To be honest, don't expect much. My iPhone 4S shows 20MB down and 2MP up and my iPad 3 shows 14MB down and 2MB up. But the ping times are similar 15ms vs 14 ms. If you were to see high ping times after multiple tests on your iPad 3, that might be a hint of trouble.

Worst case scenario, you could bring it to the Genius bar at Apple. But that's always a pain.

I've had issues with my device sending video to my ATV3, but to be fair, I was streaming some VERY high bitrate videos to the iPad 3 (and iPhone 4S) and they were both choking when I told it to send to the ATV3.