Basically, the relative magnitude between process and measurement noise determines how much to trust a new sensor measurement. In one extreme, if the process noise is zero the kalman filter will effectively ignore new sensor measurements because you've told it the process model is perfect (i.e. zero noise).
At the other extreme, if you set the process noise very large and the sensor noise very small it is like resetting the state to match the sensor reading. If your time updates happen at the same time as sensor updates, then this is effectively the same as just using the sensor without a filter. If your time updates happen faster than sensor readings, then you'll see the state drift according to your model during time updates and then do a sharp reset when the sensor reading arrives.
In practice you likely have a noisy sensor and probably don't want to follow it exactly so you need to keep the sensor noise magnitude sufficiently large. If the system is drifting too much because of inaccuracies in the process model you add more process noise until you hopefully reach a happy medium.