Well, let's recall what it means to pass a variable as constructor parameter: You initialize an object in order to use its instance variables in methods of the object. The point is that you probably use it in more than one method since you want to have a high cohesion in your class.

Passing a parameter directly to a method means in a way sending a message to an object and probably receive an answer. By that, the client wants the object to do a service for him.

So in conclusion, those are two very different means of passing parameters and you should choose whether your object should do a service or provides some functionality inherently and therefore manages some data.