Using Cap's categories from the Hansen vs Bryan thread.
Top Matches: I would give the slight edge to Bret. Bret had 3 matches make the GME top 100 and 7 others receiving votes. Savage didn't have any matches make the top 100 and only 6 total receiving votes. I suspect Savage could close the gap with more of his ICW footage, and honestly I'll probably end up voting for at least 2 more Savage matches that didn't get votes next time. Bret's best stuff vs Austin, Owen, Davey, Taker etc is outstanding. But Savage has truly great stuff with Lawler, Steamboat, Warrior, Flair, Tito Ron Garvin, that Tenryu match etc. Slight edge to Bret but it isn't overwhelming.
Versatility: I would go Bret here. Not just versatility in his work, but versatility in the roles and characters he played. Savage was pretty much always Savage both in terms of ring work and persona. Now, I wouldn't change one single thing about Randy Savage. But I don't think he had the versatility of Bret.
Consistency: I would give it to Savage here because his presence and energy could make an otherwise nondescript match entertaining/worth watching. While an average nondescript Bret match is just a boring nondescript match you wish Bret was trying harder in.
Charisma/It Factor: Savage above everyone in history except maybe 5 people and maybe not even them. Sorry Bret. I'm of the generation that grew up on Bret and his charisma absolutely works for me. But calling this for Bret would be outrageous.
Promos: Savage. Bret's best work during the USA vs Canada feud is outstanding. Some of the best mic work/outside of the ring/acting in wrestling history. But I find him pretty hit and miss outside of that run. Neidhart was probably the best part of the Hart Foundation tag team promos. Bret's singles promos pre USA vs Canada are hit and miss. Probably more hit than miss. He's definitely good. But again, this is a category where Savage is going to beat most people in history just by virtue of being Randy Savage. So compelling and charismatic that even when he was rambling coked out of his mind you couldn't look away. I include all the non-wrestling stuff in this category so you're looking at stuff like the Flair feuds in WCW & WWF, the Warrior post-match, the Steamboat angle & promos. The Jake feud. Savage belongs in that Arn, Lawler, Flair, Funk, Peak Foley category of best promos ever.
Elevating Others: I'd go Bret here. The best example of Savage elevating someone is actually the Bret SNME match. Savage was always in a featured spot against well established opponents, many of whom were good to all time great workers. Bret got saddled more often in big positions working with limited opponents or guys lower on the totem poll. You could argue that Savage's larger than life persona made all of his matches feel bigger and more important than your average pro-wrestling match (even one with a big wrestling star) so he kind of elevated all of his opponents. But I wouldn't push that as a way to say he's better than Bret. Bret's work with Owen, 123 Kid, Diesel, Yokozuna, Razor, Hakushi, cracked out Davey Boy, Undertaker when no one had good matches with him, Backlund in 94 when he made his comeback. This is probably Bret's biggest strength.
Offense: Savage. More exciting and dangerous. Bret's execution was always better of course. But Bret's offense was pretty dated whereas Savage in the early-mid 80s was one of the most dynamic male offensive wrestlers on earth.
Selling: Also super close. My gut reaction is to say Savage. He's specifically one of the best body part sellers ever. But Bret's really great too. I'm going to cheat and call this one a draw.
Rewatch Factor: Savage. These two guys are probably the main reasons I'm a wrestling fan today and stuff like Savage/Warrior and Bret/Owen are matches I've probably watched over 100 times over the course of my life. I went with Savage because I just think its more likely I'm going to find something I forgot about like the Tenryu match or something that's just new that will be unearthed. Outside of that Tom MacGee match, when was the last new really good Bret Hart match to become unavailable? 1999?
Bonus Elliott's Question: (Brody v Nigel)
This is just going to work as the stand-in for best match or work while associated with a bad wrestler because it delights me
I guess this would be Savage/Warrior vs Bret/Cracked out Davey or Sid or Nash. Either way, Savage/Warrior is the answer.
Finally tally
Savage - 7
Bret - 3
Draw - 1