While SimMechanics and Bullet are both very reliable resources, in my experience, they serve different purposes. SimMechanics is more of a scientific environment as compared to Bullet which is a real-time high-performance Physics engine.
You can rely on both of their measurements and observations but the system modeling step determines the reliability better. SimMechanics is optimized for accuracy while Bullet is optimized for performance with some allowed approximations.
In SimMechanics, you can import CAD models and all sorts of design parameters and constraints, making the simulation very well defined. While the same can also be done in Bullet, it is more cumbersome and involves manual modifications which can be difficult to handle. The ability to import CAD models through SimMechanics and have more granular control on all factors gets it the upper hand. Sensors and physical world to electrical world and vice-versa conversions are also supported, giving you more options to replicate real world conditions.
While SimMechanics trumps Bullet for your application (assuming you only need for a prototyping kind of application), the latter is the best one for production environment.