Inertial Sensor vs PID

Yes and no. I think both return the same degree of precision or at least more than you’ll need for a robot. Both are prone to drifting, but it’s been reported that the IMU drifts less. Correcting for drift has something to do with integrating error over time from the drift rate calculation during calibration (or something along those lines). I haven’t done this so don’t ask me how it works, but I have used the IMU for over a year now and haven’t really had any serious issues.

There’s more thorough discussion here, but you can always ask @jpearman for specifics