I dunno, Ten's overriding characteristic to me seems to be emotional inaccessibility (and dickitude). Honestly, I wouldn't wish him on anybody! I'm looking forward to Donna slapping some sense into him. Possibly literally.

Tennant and Tate like each other a great deal, so that should help with the chemistry. Although Tennant and Piper liked each other a great deal, and....erm. Okay. Maybe that's not a guarantee.