Apples-to-apples needs same trend fn form between cases?


A rather conceptual question, if someone could perhaps illuminate:

I am investigating possible correlation between an independent and dependent variable, for various alternative cases. (Building heating energy consumption vs a construction parameter, in various alternative locations.) There are roughly 20-30 data points in each case. I am using excel to fit a power function (y=a*x^-...) trend line. In some cases an exponential or logarithmic trend line gives a better fit.

Does it make sense to compare the best-fitting trends in these alternative cases, when they are not all using the same type of function for the trend line? Should I rather be sticking to a power function for all cases for an apples to apples comparison?

Thank you