My situation is somewhat different from yours -- multiple smaller firms (architect, structural, MEP, interiors) -- working on the same Revit models, but see what this is worth. For us, Autodesk's BIM 360 is working very well. The files are on an Autodesk server (Amazon web services, I guess), not our own local servers. Usually, the structural engineer links the architectural model into the structural model, and the architect links the structural model into the architectural one, and each manages their own details and sheet sets.
After the model is uploaded to the cloud and users invited to the project, they can all (apparently) access the same model simultaneously. In fact, they are each working on a (hidden) local copy which is then synchronized every so often with the main model, uploading their changes and downloading the changes of others. It's pretty slick. The synchronization is very quick, like 10 or 15 seconds, because only the changes are passed up and down, not the whole model. Each workstation runs a small Revit Accelerator background app that manages that process.
Also, CAD and PDF links and images for materials and decals can be saved to the same BIM360/ cloud folder as the model and so are available identically to all users, thus avoiding the problem of trying to create identical hard-wired file paths on different systems.
A happy camper here.
In several years of my experience, the servers have never gone down, and even if they did, users can keep working on their own local copies until contact is re-established, then synchronize.
My cost for this is about $900 per seat per year. With dozens of users, I bet you get a price break.
