Notifications on iPad but not iPhone or visa versa

While I’m using my iPhone I’ll get occasional notifications only on my iPad that’s asleep (nothing on my iPhone). Or visa versa… I’m using my iPad and only get a notification on my iPhone that’s asleep (nothing on iPad). This happens in all apps including Messages and Mail. It’s extremely frustrating because I’m not getting important messages/email on time and my associates are getting fed up with my excuses for responding late. Any idea how to fix this problem?