Q: Why is the DVD quality lower than m4v files?

I was asked as a parent volunteer to help with a small organization.   I videotaped a performance and then I used FCP and Compressor to create a video file (m4v).

The quality of the video was pretty good.    However, when I tried to create a DVD using the master file, the quality of the video was clearly not as good as the m4v file.

Is this an obvious fact that I'm simply not aware of?     Or am I doing something incorrectly?

Because the quality of the video was very important, I simply burned the m4v file to a DVD and asked the parents to view it on their computers or to view it on their TVs via their computer.

It isn't the best scenario so I'm asking for your input.     IF I can create a DVD whose video quality equals that of an m4v file, I'm all ears.

Thank you for any suggestions/ideas you may have.