I agree that, in general terms, a basic med exam is at least as good as a class 3 exam, and even better if conducted by your regular physician who is more familiar with your health, but as an example to address your question:
Kidney stones are not an item requiring an SI prior to Basic Med, but under a class 3 the FAA may require an SI involving extensive and regular tests. Basic Med circumvents this evaluation by a medical examiner.
I had a stone shortly after getting Basic Med, and the subsequent procedure found 3 stones which were treated. Basic Med does not require an AME or OKC to look at that condition. Furthermore, since the Basic Med exam is on a 4 year cycle but the form only requires a 3 year look-back on physician visits, my stone and procedure don't even have to be reported to my Basic Med physician at my next exam.