The real advantage to the shotgun for predator hunting is being able to hit fast moving critters on the run, or bust them at close ranges where you have minimal time to get on target and take a shot. Sure you can probably roll one at 70 yards but you’re going to need a follow up shot or two. In brush country shotguns are king, guys that only hunt fields not so much. Given that, you want the highest count of lethal size pellets possible. Which is why #4 buck is arguably the most popular, followed by T or BB shot. All have pellet weight’s heavy enough to carry their energy downrange and be lethal in minimal numbers (8 hits + on a paper plate at 50 yards seems to be the consensus for lethality.
The real equalizer for range is what the pellets are made out of. The premium stuff which is tungsten based will carry energy a lot further than lead, which carries it’s energy further than steel. The new TSS (tungsten based) is the heaviest out of them all and some people say #2 bird is lethal out to 70 yards, but who knows.
I see no advantage in going with 00 buck, just doesn’t make any sense. Also, your set up with a load in your gun anticipating them running you over, as in shots within 40 yards or so. You're not going to say, hang on a minute let me throw in some 00 buck for that 70 yard shot. Most places you'll be setup with a shotgun you can only see 40-50 yards max, if you can see further carry a rifle aswell.