I've only flown the SE cousins to those two - found both/either to be nice planes. Stick vs. Yoke is personal preference. "Pop-top" entry and wrap-around window vs. single-door and split "B-17" windscreen (and cabin width) favors the Diamonds. Those big ol' "down by the knees - handful of throttles" in the DA will generate good "muscle memory" if you're planning to go all the way to jets.
I am intrigued that you got advice that the PA44 was "great to learn the hard stuff" - since it has counter-rotating props, which removes the chance to explore/experience the issues of a "critical engine."
That's for training - if I were buying one I'd get the Piper.