FAQ
If you are a robotics control person, drake is for you. Drake has a dedicated team working on multibody dynamics, planning, and control. Drake has a whole bunch of tools that help ease the development of robot control.
Drake has a software stack similar to ROS, but it's more professional. It could compute planning based on optimization, it has a controller that handles robot dynamics rather than just PID.
So if you really dig deep into robotics and use advanced planning and control, Drake is probably a better tool.
Drake tries to incorporate optimization and contact rich simulation which is not seen on the market.
Matlab Coder is more like generate code for running on an embedded system.
If you do need to use optimization or contact is happening a lot in your model, you should consider using Drake. Drake is free.