I am trying to compare 2 random binary samples, and I am confused on which test to use.

This is to test the effectiveness of an algorithm in identifying risk factors in patients.

If the patient is diagnosed with at least 1 risk factor that is a success (1) and if they are not diagnosed with a risk factor that is a failure (0).

I have a random sample of 200 patients that were chosen prior to the algorithm being implemented and a random sample of 200 different patients that were chosen after the algorithm was implemented. I would like to compare the two samples.

I am questioning whether to use the Binomial Exact Test with the testing mean as the mean of the pre-algorithm data, or whether a Fisher's Exact Test (or any other test) would be more appropriate?

Any insight that anyone could give me would be greatly appreciated!