The exact same thing happened my Freshman year on 100 (2005).
I was a rookie then. But our team was in its
10th year!
A mentor built one design and we, the students, built a different one. The situation you describe sounds pretty mellow compared to us. I'm talking all out war between students and adults. It was ridiculous. People even cried

It nearly ended the team.
We shipped the mentor built robot. It failed. It could barely move
What little respect we had left for that mentor vanished and we unanimously booted him off the team the next year.
But strangely enough, we all learned more that year then any other year. Looking back, I'm always amazed how dedicated we became when we, the students, were working against a common enemy.
So did we really fail? I don't know.
Well, I decided to become an engineer. I got inspired. I learned how NOT to design a robot. I learned about what happens when you aren't organized and people don't cooperate. In short, the FIRST message prevailed.
Ironically, I learned a tremendous amount from that mentor, despite the fact that he drove our team into the ground.
My advice to you?
Act like engineers and pick whichever design works best. Solve the problem. No matter what happens you'll still have learned something
