Woo-hoo! I love the oath. But I agree, it somehow seems like a telling change that in the first oath they're both doing it together. "We too" shows Bruce already thinking of Dick being, if not an equal partner, someone with the same commitment. In the second it's more like he's testing Dick.
But either way, they're both awesome and I'm so glad they kept Bruce's lines about leading a perilous life. Their meeting can stand a little old-fashioned, dramatic hero language. They'd both want it that way.