Echo is almost always caused by feedback in the microhone (yours or the far end). Stutter is usually an indication of a bad network connection.
Since the iPad Air works fine, it’s probably not the far end, and it’s probably not the network connection. Though you should check to see if your iPad Pro is getting a good connection to your wi-fi.
It’s also possible the app or iPad itself is behaving erratically. So, back to basics.
If you have not restarted your iPad Pro recently, do so. Be sure to actually turn it off (press the power button until the ‘Slide to Power Off’ button appears, and then slide off. Just tapping the power button to turn off the screen only enters sleep mode.
You can also try deleting and re-installing the Skype app. If the app has been corrupted, this should fix it.
I don’t have any other ideas.