Trust as a contractor can be an interesting thing. On one hand they may not trust you because you are an outsider who they think can't possibly understand the nuances of their culture and business domain, but on the other hand they will often deliberately trust you on technical matters because you are bringing outside perspective. Point being - you may get more of the opportunities you want by virtue of being a contractor.

That said - I'm not completely sure what you are really after here. When you talk about wanting to be something more - like what? You want to be an architect? You want to be in management? You want to be a subject matter expert? Product management? I wonder if either a startup or a large corp would be good for you... what I mean is, let's say you are early at a startup. Well, you get to do a bunch of everything because there's no one else to do it. Alternatively, big corps can be a great place to spend a year in this team, a year in that team, and give people lots of experiences in one place, where each role builds on the next - assuming you are managing your career and don't get stuck somewhere. Not sure what's the right option for you, but I'm assuming you'll run with this and figure it out.