Those 2 are mega-amped versions of comic characters based on their game character counterparts.
I don't know if such a thread is allowed. Meh.
Seeing as we don't know the full extent of Chaos Knuckles' abilities even though he's likely the most powerful entity to appear on Mobius, Titan Tails probably wins. TT was a merged form resulting from the fusion of every single Tails in the multi-verse I believe.
Chaos Knuckles at full power would stomp Titan Tails IMO.
Chaos Knuckles was never empowered by the Master Emerald. It is basically his true form, i.e. his own untapped power.
Besides, such a correlation really doesn't speak anything about the power levels of the two. Not to mention, Chaos Knuckles would easily stomp Master Mogul if they got into a true fight.
^Well, it goes like this for Chaos Knuckles: before he was born, his father exposed his egg to the radiation from a Chaos Emerald. This in effect made Knuckles become one with the Chaos Force (as I believe they call it), and thus he would eventually be born with powers beyond anyone else known to use it.
Chaos Knuckles actually fought Mammoth Mogul, but was tircked into going into some sort of place that started to sap his powers, so Knuckles powered up past his limit, killing himself in the process. When he came back to life (the process of which I think actually is what made him "become one" with the Chaos Force), he supposedley lost these powers, but it was eventually revealed that they were just dormant. I think it wasn't until then that he became Chaos Knuckles again due to exposure to the Master Emerald, which kinda reawakened them. I don't know if it made him any more powerful than before.
But didn't some form of Tails fight Knuckles as the second Enerjak and still lose? I'd been on the assumption that Enerjak Knuckles-whom, to my recollection, had beaten both Sonic, and a ringless Shadow at the same time-is weaker than Chaos Knuckles. But again, I could be wrong.