That's weird. Can't say that I've noticed it in Lemire's JLD, but then I never did read Milligan's JLD and I don't have that much exposure to Constantine but I'm aware of his character and some background.
Do you have any examples?
I don't have the issue with me anymore - sorry. But like I said: it's not a super concrete reaction... more of a visceral "yeah, John wouldn't talk like this" than anything that I can articulate.
It's not a big deal if you don't notice it, though.