I think both versions have top-notch casts. Lippa's version (cast recording-wise, haven't seen it live) has Julia Murney's haunting Queenie at the center of the show surrounded by great performances by D'Arcy James (why is he so underrated?), Taye Diggs (even if he is not as enigmatic as Yancey Arias comes off in the LaChiusa recording), Idina Menzel (I find her to be giving a really fun performance on the cast recording even if her--and Lippa's--version of Kate lacks the kind of edge, sexiness, and insecurities that LaChiusa and Tonya Pinkins added to their version of Kate), Alix Korey, et al.
LaChiusa is to me more fulfilling in terms of the nuances in the score. "People Like Us," "Queenie Was a Blonde," "Wild Party," "Welcome to My Party," and "Best Friends" are just really fascinating, thrilling--some heart-breaking--pieces. Toni Collette, Mandy Patinkin, Tonya Pinkins, and Eartha Kitt are great on the cast recording. LaChiusa's is my favorite but I don't think Lippa's is bad.
"Some people can thrive and bloom living life in a living room, that's perfect for some people of one hundred and five. But I at least gotta try, when I think of all the sights that I gotta see, all the places I gotta play, all the things that I gotta be at"