Stipe has two strengths: good power in his hands for a HW and decent wrestling.
CC (in 2005) had four strengths: excellent TD defense, HW power in his hands, unmatched power in his kicks, and he was extremely elusive (rarely got hit) and he even had one submission win.
Probable outcome: CC KOs Stipe with a kick.
I agree with TS though, HW has devolved. Even the most well-rounded of all current HWs (Werdum) now thinks he is a boxer.
My assessment of the state of HW: a bunch of would-be boxers with bad cardio.
Cormier vs Stipe outcome: Stipe wins by KO, or DC grinds him out.
Likely outcome: Stipe by KO because if DC can't handle JJ power, there's no way he'll be able to take a shot from Stipe... now, the HW DC from Strikeforce would absolutely manhandle today's Stipe. But I don't think DC is anywhere near as strong as he used to be (and his raw strength is why he was able to dominate guys like Barnett)