For a more sophisticated theory of analogical reasoning, you should read Dedre Gentner's papers. A good starting point is The structure-mapping engine: Algorithm and examples. Gentner defines a hierarchy of attributes (properties of entities; in logic, predicates with single arguments, P(X)), first-order relations (relations between entities; in logic, predicates with two or more arguments, R(X,Y)), and higher-order relations (relations between relations). Her experiments with children show that they begin reasoning with attributional similarity (what you call "surface similarities"); as they mature, they make increasing use of first-order relational similarity (what you call "structural similarity"); finally, they begin using higher-order relations, especially causal relations. This fits perfectly with your description of your own childhood. See Language and the career of similarity.