Nemesis: Martian Manhunter
Other Major Foes: JLA, Plastic Man, Scorch, Vandal Savage, & White Martians.
Appearances: 6 original comics
Powers: Super strength, speed & senses, shapeshifting, density control, flight, invisibility, telepathy, nigh-invulnerability and fire generation/control.
Fernus was a prehistoric Martian from a time when the race were demonic flaming creatures who was killed by Vandar Adg and resurrected thousands of years later in the body of J'Onn J'Onzz. The Burning proceeded to murder as many White Martians and henchmen of Vandal Savage as he could get his hands on before brutally defeating the JLA and attempting to destroy Earth. Fernus was finally halted by the combined efforts of Scorch, Plastic Man, and Martian Manhunter.
Win: Effigy (10-2)
Lose: Darkseid (6-8); Malefic (5-18)
Nemesis: Green Lantern
Other Major Foes: Every light spectrum corps in the DCU
Appearances: 500+ original comics, numerous animated series/features, live action television, a major motion picture, toys, video games and more.
Powers: A power ring which creates potent hard light constructs and can absorb/project massive amounts of energy, as well as providing interstellar flight and impressive defensive capabilities.
Sinestro was considered the greatest of the Green Lantern Corps before his perfectionism turned him into a fascist. Ejected and incriminated, Sinestro allied with the Weaponers of Qward, who created a yellow power ring that fed off and exploited an essential vulnerability in his former corpsmen's green rings. Sinestro was the Lanterns' most tenacious foe, and eventually formed his own corps who were motivated to instill fear.
When I was a kid, I couldn't understand why Green Lantern wasn't the most powerful mainstream DC hero, since he had a ring that could basically duplicate any power plus create energy constructs like force fields. However, besides the very dumb advantages taken against the ring with literally anything colored yellow ("the bananarang penetrated Lantern's shield and knocked him senseless") the constructs could simply be overwhelmed by a superior force (like Superman.) Martian Manhunter's (pale shadow of) near Kryptonian powers would presumably fall into this category, but the Alien Atlas was an even more ineffectual protagonist than Hal Jordan, thanks to his extremely pacifying issues with flames. Green Lantern Alan Scott routinely manifests his powers as flames, so that wrestling match would be over at the introductions, much less in the ring.
In the cases of Fernus and Sinestro, to quote Blade II, you have representatives with "all of their strengths, and none of their weaknesses." Fernus eats, poops and breathes fire, while Sinestro has a yellow power ring that slurps Green Lantern juice, hold the weaksauce. Both of these dudes have full command of their extraordinary abilities with none of the foolishness of their heroic counterparts. The advantage I see for The Burning is his ownership of the JLA, something I cannot recall the Korugarian ever pulling off. Sinestro was created to battle Hal Jordan on a consistent basis, and has tended to pull in helpers when he's needed to deal with more than one Green Lantern. Sinestro was also a member of the Legion of Doom in animation, and the Secret Society of Super-Villains in comics, which further solidifies him as a guy who needs to work with a team. Fernus worked over the Magnificent Seven JLA and satellite members all on his own, and was on his way to annihilating the human race if not for some last minute betrayals and deus ex machina. Regardless of the Parallax avatars standing and visibility, this match is the Martians' to win.