One of the reasons that I believe, and even most powerlifters believe, that strongmen are stronger isn't just because of deadlifting. And though that's certainly a great indicator, I will say that the reason most strongmen are great pullers is because well, top level strongmen are built for pulling (duh). Tall, long arms, strong backs.
However, one of the reasons I believe that strongmen are stronger than powerlifters is because they have to get strong in a variety of ways, using a variety of implements, and in a variety of movements.
A very prevalent thing I see in powerlifting is guys who can maximize leverages to "appear" stronger than they really are. There's going to be people that take offense to that, but I give no shits.
You are most definitely supposed to use your leverages to move more weight, without question. However one of the reasons that a LOT of guys end up spinning their wheels in terms of strength and muscular development over a long span is because they just keep trying to use their leverages, and stop trying to get stronger.
"Well I don't need to overhead press at a meet". Yes, I know this, however your bench hasn't moved in a long time. It may be that you've maxed out your leverages at this boydweight for that movement. Or it may be, that other areas of your musculature need to get stronger in order for you to get past this plateau. It's probably a combination of both.
Any "advanced" strength athlete should be able to clean and press their bodyweight for reps, pretty easily. If you can't, you're either too weak to call yourself advanced, or too fat for your own good.
You should be able to do 20 bodyweight chins. You should be able to front squat 80% of your back squat.
I've seen so many guys talk about "weak point" training and sound off on bullshit like "my lift stalls here, so I need to overload that part of the range of motion to beat that sticking point." No man, you just need to get fucking stronger. I've never ever seen a guy do board humping with less weight than he could bench. That alone should tell you that you're not weaker at the transition point. You miss at a certain weight because you're not strong enough to generate enough force out of the bottom to overcome that transition. So simply put, get stronger.
You should be strong in any plane of pressing. Overhead, incline, bench.
You should be strong front squatting AND back squatting. If you squat low bar normally, do high bar squats. It'll suck, but when you go back to low bar, you'll be even better.
You should also spend a significant portion of your offseason with no belt, no wraps trying to work up to your best set of squats, repetition wise, when you use those.
You should focus on stiff legged deadlifts and building a bigger and stronger back. Make it a point to program your barbell rows and don't slack on your back work.
If you wanted me to tell you one secret to getting to a next level for yourself, it's to become well rounded. You don't need to do a million movements to be well rounded. It doesn't mean you need to have a bunch of special bars or add eleventy billion pounds of band tension to the bar. But you should be well rounded with a barbell through multiple planes and types of movements. This will fix "weak points" and boost your big three. Strongmen know they can't just rely on learning leverages. They actually have to get fucking stronger. Think in terms of becoming a brute from top to bottom, and make it a point to get strong overall.
Clean and press, press behind the neck, incline, front squats, stiff legs, sumo pulls, block pulls, db pressing, various chin ups, all forms of rowing, curls. Get strong with the BARBELL. Get strong without any support on. Get strong with dumbbells. Put yourself in a mechanically weaker position, and when you go back to your stronger position, you'll be even better. Then you can really focus on maximizing your strengths. However now, you'll be well rounded and brutally strong from top to bottom.