In general, one could use any CDF with support R as index/link function for a binary response. The main advantage of logit is the interpretation. We are modeling on log odds. This idea is easy to sell in analytics. But in case of probit, we can't bring this relation.
Also in GLM, when you assume logit, the mean, variance of the beta estimates can easily estimate compare to probit.
When you compare the fitted sigmoid curve, there is not much difference between probit and logit( in my experience). data may suit probit or logit, but logit can interpret well the structure. So my vote is for logit.