The short answer is: probably not.
I have seen Quest and LabCorp widely used in hospitals. If you look at the bottom of each organization’s page, there should be a credentials or certification that they are each certified through. Search the credentialing agency and see if they are legitimate (with Britannica or other encyclopedia). There may be very small differences in level of accuracy but they generally all have to meet a minimal acceptable standard.
I would not view it as a difference in accuracy, but you would likely get different numbers because these lab companies may have different methods of testing the same thing.
For example, let’s say that you needed to check your sodium level. The same blood sample sent to Quest may come back as 140 with a reference range (normal range) of 135-145 whereas if it was sent to LabCorp it may come back as 137 with a reference range of 130-143.
There would be no clinical difference between those two values because both are within the normal spectrum. The range of normal spectrum though can differ depending on a company’s method of testing.