Can I transfer everything from my old iPhone to my new one if I share and Apple ID?

My dad and I both share an Apple ID. When we upgrade our phones in a couple of months, can we get our own stuff on each of our phones, or do we both get all of the apps from both phones?

If you guys are under the same itunes account then you will get everything on your old phones back the same

Yes as long as you keep sharing the same Apple ID.

Your phones should be taking backups automatically to iCloud, unless you've turned that off, so it will be easy for both of you to restore your respective backups to your new phones, and they'll each be set up just like the old ones. It only takes twenty minutes or so.