Compare coefficients of two regression models


I have a little problem I hope someone can help me with.

I run 2 multiple regression models with the same independent variables but different dependent variables. Now, I want to know if one of the independent variables, say IV1, has a stronger influence on the first dependent variable than on the second.

In my model, the coefficients for IV1 are 0.9 and 0.1 and both are significant. But to my understanding, I cannot simply assume that 0.9>0.1 since it depends on the characteristics of the dependent variables? Is there any common method how to compare coefficients of two regression models? I only read something about standardized coefficients, but that seems more to be about the comparison of IV's of the same regression model with respect to the measurement units.

I hope my problem is somehow understandable and someone can help me.

Thank you! :)