Well back when he encountered Ling when he took down Lan Fan, Ling managed to escape and Bradley mentioned that his age had worn him down quite a bit.
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Speedwise there's no doubt that Bradley was much faster than Ling, so I'm pretty sure what it comes down to is his body's lack of stamina due to old age.
And killing Pride enough times to put him down permanently would probably require even more effort than his battles against them, not to mention that Pride's attacks pack a lot more power than any of theirs and if he actually gets a hit then Wrath can't just shrug it off. Both his shadows and Kimblee's alchemy could prove deadly against Wrath and even a single hit would be much harder to come back from than any of the attacks from Greedling or Scar.