Sensitively and specificity

Which one is the best to choose…

A test with high specificity and low sensitivity.

Or, a test with a high sensitivity and low specificity?

And why?

There is a tradeoff between the sensitivity and the specificity, the higher one of them, the lower the other.
Therefore the choice defends on what’s important to you:
If it is more important to have a higher probability of positive diagnosis given the patient is positive then you should lean to higher sensitivity. On the other hand, if it is more important to have a higher probability of negative diagnosis given the patient is negative then you should lean toward higher specificity.

That leaves us wanting to know if sensitivity and specificity are useful. I think not. They condition on the unknown to compute probabilities of the already known quantities (test results). Once you have a diagnostic probability model everything is direct, and developing such a model can avoid sens and spec unless doing a case-control study. More at fharrell.com/post/backwards-probs