The crucial useful thing in the club system is the fact that logical harmonies are easier. For example, on an ordinary D/G box. on the bass buttons in the key of G, you get a D chord on the pull, put the D melody note is on a push. Incompatible, you see. But with the club system you can get that D melody note on the pull or push. Which gives great flexibility whether you harmonise it with a G or D chord.
    Also, in melodic terms, with the Club system you can get the whole scale of G on the pull, which greatly facilitates playing smooth runs(if that is your taste).