Are there rules of thumb that help determine which to use in what case? Should I prefer one over the other most times?
Thanks!
I would stick to inheritance except in the cases that extension methods were primarily designed for - extending sealed classes or creating scope-specific extensions. Also remember that they are static, so if these are methods and behaviours that you would need to override in other classes, you can't really use extensions.
Extension methods do have one really great feature that is an inherent benefit of their implementation. Since they are static methods, you can call them on a null object.
For instance:
string a = null;
return a.IfNullOrEmpty("Default Value");
Implementations like this are great, though they are technically just syntactical sugar. IMHO, anything that keeps your code cleaner and more readable is great.
Though I don't like that they aren't really discoverable. If I copy that code from one class to another, i would then have to search for the namespace in which it was defined.