Magnet Pull is easily a better ability than Sturdy. Magnet Pull gives Magnezone a very important niche as perhaps the game's most assured counter to Corviknight and Skarmory. This means Magnezone has really strong synergy with Pokemon like Rillaboom and Hawlucha, who can sweep more easily once those Pokemon are taken out. Sturdy is a decent ability, but it can't match the value of trapping the opponent's Corviknight.
The real competitor to Magnet Pull that you didn't mention is Analytic, which is itself a very strong ability. Analytic was mostly out of the equation when Magnezone had HP Fire, but now that Magnezone can't put all its eggs in the 'kill every Steel-type' basket, it has become more enticing to increase Magnezone's wallbreaking ability against other Pokemon. Here are some calcs that show how common Magnezone switch-ins get worn down by Analytic-boosted attacks; if these look enticing to you, then maybe give it a try.
252+ SpA Choice Specs Analytic Magnezone Flash Cannon vs. 252 HP / 0 SpD Hippowdon: 366-432 (87.1 - 102.8%) -- 56.3% chance to OHKO after Stealth Rock
252+ SpA Choice Specs Analytic Magnezone Flash Cannon vs. 0 HP / 0 SpD Zeraora: 168-198 (52.9 - 62.4%) -- guaranteed 2HKO
252+ SpA Choice Specs Analytic Magnezone Thunderbolt vs. 248 HP / 0 SpD Rotom-Heat: 148-175 (48.8 - 57.7%) -- 96.1% chance to 2HKO
252+ SpA Choice Specs Analytic Magnezone Flash Cannon vs. 248 HP / 88 SpD Amoonguss: 303-357 (70.3 - 82.8%) -- guaranteed 2HKO after Black Sludge recovery
252+ SpA Choice Specs Analytic Magnezone Flash Cannon vs. 252 HP / 4 SpD Seismitoad: 177-208 (42.7 - 50.2%) -- 37.9% chance to 2HKO after Stealth Rock
252+ SpA Choice Specs Analytic Magnezone Flash Cannon vs. 248 HP / 0 SpD Excadrill: 199-234 (47 - 55.3%) -- 41.4% chance to 2HKO after Stealth Rock and Leftovers recovery
Otherwise, Magnet Pull is the way to go. If you're not looking specifically for a wallbreaker who can open up balance cores involving Pokemon like Clefable, Corviknight, Mandibuzz and Toxapex, then you might want to use a different Pokemon entirely. Zeraora and Rotom-H are better 'generalists' because their coverage and speed lets them play as offensive pivots.
Here are some usage stats. In July (i.e. before the Cinderace and Magearna bans), Magnet Pull was used by 73% of players with 1825+ Elo, and Analytic by 26%.