[Chris is me]

In my opinion CAD is absolutely essential to becoming a competitive robotics team. Detailed design is just so much easier. Seeing how things will work and fit together before building them is priceless. Iteration after build season is sometimes only possible by referencing your model robot. I would definitely get your team on track to use CAD for the next build season if you want to build competitive, professional robots.

Inventor vs Solidworks is like PC vs Mac. They both do the same job fairly well; it comes down to personal preference and what is used by schools / companies related to your team.

If you have any sponsors for manufacturing metal equipment, use whatever program they prefer. If you don't have manufacturing sponsors, they're cool and you should get some!

If the above is not a factor and your school teaches a specific flavor of software already, use that. Shaker High School teaches Inventor as part of its pre-engineering program so we use Inventor.

All other things equal, I think Solidworks is both easier to learn and more powerful / flexible and would choose that. However the constraints of your school and sponsors are more important than preference.