Regression with log-link is useful for studying the relative change in an outcome variable.
In a log-link regression model, the antilog of each coefficient represents the independent association of that covariate with the relative change in the outcome variable, holding all other variables constant.
Logistic regression is useful for studying associations for a binary outcome variable.
In a logistic regression model, the antilog of each coefficient represents the odds ratio of that covariate with the outcome variable, holding all other variables in the model constant.
In log-link and logistic regression models, the null hypothesis for a covariate is that the antilog of the coefficient for that covariate equals 1.0.