Lumia 940? You probably mean 930 or 640. Also it would be necessary to know which OS build you are running?
Is the old account on windows phone 8.1? Did you run Windows Mobile 10 Insider builds on it?
On the 950, what build are you running? Did you update the Mail and Calendar app from the Store to the latest version?
Also did you compare the settings on both the old end new setup?