As far as copyright goes, Jack belongs to Russell T Davies—you can tell that because Steven Moffat receives no character credit for him on Torchwood.
But it's hard to say whether Russell T Davies or Steven Moffat had more of a hand in defining Jack's personality and the details of his character. Davies invented the character, but Moffat wrote his first story (The Empty Child/The Doctor Dances). And in Davies' book The Writer's Tale, he explains how he heavily rewrote almost everyone else's episodes, but gave Moffat free reign. So, when he decided he wanted Moffat to write Jack's introductory story, he apparently intended to give Moffat a hand in designing the character.
Some of what we know (from the accompanying Confidential, The Writer's Tale, and various interviews):
Davies wanted an 'exotic' companion to balance out the 'viewer-identification character' of Rose. He chose the name 'Jack' because he wanted a solid, thoroughly English name. He made Jack a Time Agent from the 51st century as a continuity reference for fan geeks like himself (the Time Agents were first mentioned in 1977's The Talons of Weng-Chiang, and later fleshed out in various novels). He wanted Jack to be a 'renegade' Time Agent as a parallel to the Doctor (a renegade Time Lord), but apparently Moffat is the one who fleshed out that idea into making him a con man. Davies wanted the character to be blatantly omnisexual, and to compete with Rose for the Doctor's affections, but Moffat came up with the idea of Jack and Rose flirting with each other first, and the idea of Jack disguising his interest by teasing the Doctor about his asexuality (which led to the famous 'dancing' metaphor).
So, how much different would Jack have been if Moffat hadn't been involved? Who knows.
Given the character's subsequent appearances in Torchwood, etc., it's reasonably safe to say Russell T Davies found he could live with what Moffat had done.