The Hero's only real strength feat that I can recall is pushing through Vitiate's lightning, but it can be assumed he's physically potent enough to counter Vader's blows with at least significant efficiency. He's still at a disadvantage when comparing strength no matter how you look at it though, Vader has torn apart huge slabs of durasteel bare handed, overpowered most opponents he's faced with raw strength, and you get the idea from there.
Vader has formed shields out of his blade, moved invisibly fast, produced 4 afterimages behind his blade, and has fought in a blur. Conversely, the Hero has on more than one occasion cut down elite Sith Warriors and Assassins before they could even react, which is always a superb feat. All-in-all, the Hero should be more than capable of keeping up with Vader, though I'd declare Darth the faster of the two as well.
As far as durability and endurance goes, the Hero withstood palpable amounts of damage from Vitiate's Force Storm before going down, and likely endured significant damage and continued fighting in their final battle. Vader, however, outstrips him here too. The guy tanks lightsaber strikes and stabs mid-battle, loses limbs and keeps fighting, tanks bomb blasts at point blank range, not to mention that he's already protected by dark armor....
So basically, it's evident that while the Hero's physical capabilities are highly advanced, Vader's are significantly greater.
Now let's look at them in terms of skill. The Hero has outfought many saber prodigies. The first example being Praven, who outdueled one fo the Jedi's best swordsmen in battle, and then defeated another Sith who was considered his superior, and he did it when he was amped, too. He then goes on to outduel Darth Angral, who is Dark Council Level and easily outfought a Jedi Councillor, and he gains significantly from then on as a swordsman. Vader, however, is just as impressive. He's taken on a strike team of seven Jedi Masters and nearly killed them all primarily through saber prowess, then continued to outduel fighters like An'ya Kuro, Galen Marek, and Obi-Wan Kenobi--All of which are legendary fighters who were amongst the best of the day. Not only that, but he also gains considerably from then to his peak. Both of them use the same primary styles, (Djem So/Soresu) but Vader also incorporates heavy Makashi elements as well, and has a more unorthodox style. I could see giving the Hero the edge in terms of skill due to the unknown amount of skill he gained from Act 2 to Act 3, (Though we do know that by Act 3 he was good enough to cut down the Imperial Guard, something someone on Nyriss's level didn't even consider a possibility.) but in the end Vader's feats of skill are just as good as his are.
The final thing to consider, which is Force Powers, is honestly fairly obvious. While Vitiate notes that the Hero harnesses immense power that he can't fully control, Vader is also the Chosen One--His raw power is also absolutely immense on the same scale. As for feats with the Force, yeah, the Hero has collapsed ceilings and forced bridges to close, but Vader has collapsed cathedrals, blasted away dozens of fighters, ripped down huge contraptions, busted huge droids, and more. Vader definitely holds an advantage as a Force Wielder as well, both in power and his application of it.
In the end, the Hero is extremely powerful--The best Jedi of his day, and someone capable of defeating the guy who downed Revan. However, in a side by side comparison, it's really hard to give him the advantage over Vader--Because he hasn't really accomplished anything that Vader hasn't done better.