Previous incarnations of the Hulk would have trouble taking on The Juggernaut. For the most part The most recent incarnation though - The Green Scar Hulk - probably would win. It was stated by writer Greg Pak that Green Scar Hulk during the World War Hulk storyline was "stronger than any mortal --and most immortals-- who ever walked the Earth."
Also, Hulk was able to take on Onslaught, a dude with god-like powers, and destroy his armor, whereas Onslaught ripped Juggernaut's crimson gem of cyttorak (source of his power) out of his body, and he demonstrated sufficient strength to overpower a fully powered Juggernaut and punch him with enough force to sending flying through the air from Canada to New Jersey with a single blow.
from Marvel Database
http://marvel.wikia.com/wiki/Robert_Bruce_...er_(Earth-616):QUOTE
* The Hulk possesses the capacity for vast levels of physical strength.The entity Beyonder once stated that the Hulk's potential strength is limitless, without any limit inside [5].He has demonstrated strength greater to that of Thor's[6] [7] , whose strength equals Hercules [8].Hulk also demonstrated enough strength to overcome the Power Cosmic of Silver Surfer,who was fueling a draining machine [9].In the officially stated statistics of the "Marvel Super Heroes Game",the Hulk's potential strength was classified as Class 500,while powerhouses like the classic versions of Hercules and the Juggernaut were classified as Class 100,and the classic version of the Silver Surfer and his cosmically increased strength was classified as Class 150[10]. However, each of the "core" Hulk personalities possesses a base strength level. While in a functionally calm state, the Gray Hulk is capable of lifting 70 tons, the Savage Hulk can lift about 90 tons, and the Merged Hulk can lift about 100 tons. The current incarnation, sometimes referred to as "Green Scar" is the physically strongest of all the primary Hulk incarnations. After being exposed to energies from the exploding warp core of the ship that originally brought him to Sakaar, his base strength level was dramatically increased. While in a "calm" state, Green scar is capable of lifting well over 100 tons.
While in an enraged state,adrenaline surges through the Hulk's body, increasing his strength considerably beyond his base limits.
For example, during the Secret Wars, he was seen effectively using leverage to support a 150 billion ton mountain, which was dropped on them by the Molecule Man until the heroes buried inside could find a way to blast their way out. The Hulk also seems to be stronger with the more radiation he absorbs, which is the main reason why Maestro from the future has become stronger than the present Hulk.
The Hulk was the only superhero able to crack the armor of the psychic "Godlike" being Onslaught,demonstrating strength rivaling the entity's,after Jean Grey used her telepathic powers to effectively shut down Banner's persona[11].
* Superhuman Stamina: The Hulk's body counteracts fatigue poisons that build up in his muscles during physical activity. In an enraged state, the Hulk is capable of exerting himself at peak capacity for several days before fatigue begins to affect him. However, much like his physical strength, the Hulk's stamina does increase as he becomes angrier.
* Superhuman Durability: In addition to great strength, the Hulk's body possesses a high degree of resistance to injury, pain, and disease. The Hulk's skin is capable of withstanding extreme heat without blistering, extreme cold without freezing, and great impacts. The Hulk has withstood the impact of a ground zero nuclear explosion and the full force of the the Human Torch's Nova Blast, which is said to have a maximum temperature of 1,000,000 degrees Fahrenheit, without sustaining injury. The Hulk's durability, like his strength, is fueled by rushes of adrenaline while angry.
I think in the long run Hulk is stronger than Juggernaut...so long as he's angry enough. And honestly, when the hell is he not angry?