Just as their relationships with other costumed crusaders varied, so had the Batmen's partnership with the Robins. On Earth-One, Batman worked well with his comrades on the Justice League... on Earth-Two, Batman kept mostly to himself and suspected his Justice Society allies a time or two. It seemed the reverse as to their sidekicks, as Earth-One's Batman had a somewhat adversarial and overprotective demeanor towards his Boy Wonder, while Earth-Two's Batman was entirely supportive of his Ex-Boy Wonder.
What is interesting is how the two Batmen interacted with Earth-Two's Robin (that world's Batman never met Earth-One's Robin, unfortunately). The older Batman not only bequeathed the mantle of Gotham City protector to Robin, he accompanied him to an awards ceremony to show such support. However, the younger Batman seemed to be a bit to condescending with that Robin, even though they were the same age. Now given, he was still use to teenage college student Dick Grayson rather than U.S. ambassador Richard Grayson, nevertheless it was this same attitude with his own Dick which caused his former partner to forsake the Robin alias for that of Nightwing. On Earth-Two, his own mentor made him feel so comfortable as his own man that he never forsook his famed alter ego.