The Hulk from the Marvel Cinematic Universe is one of the mightiest heroes around, with his power increasing as his anger goes up, getting stronger with every blow and strike traded with his adversary. However, he's not truly the strongest there is.
With the new Disney-Fox merger, there's another adversary who might match the Hulk in power: the Juggernaut. The Juggernaut has made two appearances in Fox's universe. While the relatively pathetic iteration in X-Men: The Last Stand was subdued by Kitty Pryde, the unstoppable monster that appeared in Deadpool 2 might prove too powerful for Bruce Banner to handle. In fact, he might just rip the Hulk to shreds due to the fact that he's literally unstoppable.
A MATTER OF POWER
Both Juggernaut and Hulk have demonstrated incredible power over their tenure. While Juggernaut had only Deadpool 2 to show off a fraction of his abilities, Hulk reached his zenith on-screen when brawling Fenrir and Thanos in Thor: Ragnorak and Avengers: Infinity War, respectively. He was even able to hold up the whole of the collapsed Avengers Mansion on his back during the final battle in Avengers: Endgame.
However, while the Hulk is strong, the Juggernaut is literally unstoppable. Once the Juggernaut starts going, he cannot stop under any circumstances. This means that the only chance Hulk has at stopping this brute is if he can stand his ground and just trade blows with Juggernaut. That would require strategy, a trait he possesses as Professor Hulk. As the plain green Savage Hulk, however, he'll probably inadvertently play to Juggernaut's strengths, just pounding at the guy until he builds up momentum.
By contrast, Hulk can be stopped. His fight with Tony in the Hulkbuster armor in Avengers: Age of Ultron proved that metal barriers and cages can stop him temporarily. If those same barriers were used against the Juggernaut, the unstoppable force would pound right through them if he built up momentum. It's impossible to brute-strength your way out of a fight with the Juggernaut. The only solution is to use a clever strategy, one that only Bruce Banner himself might be capable of.
SHEER BRUTALITY
Let's say that for argument's sake that Juggernaut fights Professor Hulk. Professor Hulk, like Colossus in Deadpool 2, figures out a strategy to hit Juggernaut where it hurts, like shoving a live-wire up his butt while submerging him into electricity-conducting water. However, it's highly unlikely that Bruce would be able to get that far with Juggernaut when pitted against his sheer brutality.
Juggernaut's first appearance features him ripping Deadpool's body in half. Juggernaut has a reputation for cruelty, with his attacks often not only being demonstrations of his incredible strength, but also his incredible sadism. He's willing to hit as hard as it takes wherever it takes. By comparison, Hulk at his most chaotic is more into thrashing people around, swinging Thor and Loki around like rag-dolls or punching Fenrir hard in the face. He's able to smash aliens and Ultron drones to putty, but he seems to hold back against flesh and blood, choosing to punch and pound instead. While this is a good strategy against most fleshy bodies, it's ineffective against the Juggernaut.
However, even worse, Professor Hulk hates fighting. Sure, Bruce Banner in his Hulkbuster armor was able to take down Cull Obsidian, but Cull Obsidian was no Juggernaut. In Avengers: Endgame, Professor Hulk is incredibly unwilling to smash up anything. This hesitance to engage in brutal combat is a weakness Juggernaut will exploit.
ENDURANCE
Ultimately, a fight between Juggernaut and Hulk will come down to who can take more punishment. They're both capable of dishing out and dealing a lot of pain, but the only attacks that seem to affect Juggernaut are those that get under his skin -- such as electricity bombarding the soft tissue of his intestines. This would seem to indicate that Juggernaut's skin is impenetrable. Add to that a layer of armor, and Hulk is gonna have a hard time landing a good blow.
In contrast, while Hulk is powerful, he's been made to bleed several times in the MCU. Fenris's fangs managed to break his skin, Thanos beat him into submission and the cosmic force of the Infinity Gauntlet shriveled up his arm. While it's unlikely that Juggernaut would fare much better with the Gauntlet and Thanos might still be able to beat Juggernaut down, it's highly unlikely that anything could make him actually bleed like that.
The Hulk could still beat Juggernaut if he, like Colossus, learned to fight incredibly dirty. However, on his own, it might be all but impossible for Bruce Banner's alter-ego to stop this unstoppable force when he charges into the MCU -- especially if the franchise amps up his power in his eventual debut.