I didn't see anyone else reply to this post yet so I decided to do some research. From my understanding, the two experiences happen on different planes and feel quite different. Also when you Astral Project, your conscious body is outside of you whereas when you dream vividly it is still inside you. If you want more details you can message me ^^
These are pretty good answers. All in all it will feel different. When you astral project you will feel... Free. As the others said when you astral project your spirit/soul/consciousness is outside of your body while when you dream you are still inside your body.