Our team worked with 4 other teams in our area a few years back to create a non-profit organization (
FIRST of the Great Lakes Bay Region). The main benefit was that by having our sponsors donate to the organization, member teams could get funds out basically instantly (previously we had to submit receipts and wait 6 weeks to get refunded, impractical during a build season obviously).
While the organization was created as a way to escape the umbrella of school funding (while still maintaining a good relationship with our schools), having the organization run by 4 teams forced us to work more closely with each other and improve our groups coordination in our area. Consequently, FIRST of the Great Lakes Bay Region now helps support over 20 1st and 2nd year teams, a number of FLL and FTC teams, and we've hosted a District Competition and an
Off-Season Event for two years in a row. All this happened in just the last 4 years.
To answer your questions more specifically...
Did it help, or was it more work than it was worth?
There is a bit more paperwork involved, we had to create a board of directors (in our case, made up of two mentors from each member team), we are also required to hold a board meeting yearly. Beyond that though, I would say it was worth it. We do still stay active with our school, which is supportive of our team and gives us a very nice facility to work in.
What are the tradeoffs?
Honestly, the only day to day difference in the operation of our team was how we paid for things. This will likely vary depending on a teams relationship with their school though.
Was it easier or harder to get sponsors?
Though it took a few years to get our name out there, we're now starting to have sponsors (Big sponsors too) start to actually come to us without any prompting and ask to be a sponsor, either of one of our events, or to support our member teams.