It generally does not depend on the tolerance of the controller, assuming the controllers (MPNs) are the same. It does depend on the tuning parameters set in the component.
If smartsense is set as the tuning option, then some variation is expected between boards in terms of the absolute raw counts/diff counts. Parameters such as resolution might be set differently in both cases causing the issue.
Please let us know if you are using CapSense tuner to measure the diff counts in both cases. You can also use tuner to measure the SNR directly and as long as the SNR is greater than 5:1, the design is correct.