Actually, it's the other way around. While it's true that the madder Hulk gets, the stronger he gets, he also gives off increased amounts of gamma radiation as he gets angrier, which Godzilla would simply absorb. Over time, Godzilla's reaction to the Hulk's attacks would become lessened, as he would gain more stamina in response to the Hulk's radioactive output. Let's consider the "World Breaker Hulk" stage. At this point, the Hulk's attacks would be capable of knocking Godzilla out if not for one thing - the increased radioactive output which would accompany those attacks. In essence, the blow which might have allowed the Hulk to beat Godzilla would end up revitalizing Goji more than it hurts him. Therefore, the longer the fight goes, the more it favors Godzilla.
In addition, Godzilla would not have a hard time hitting the Hulk, nor would his radioactive prowess prove useless. The Hulk does not absorb radiation; in fact, he has been shown to be hurt by it. One of Hulk's alternate future selves, the Maestro, was disintegrated by a nuclear-level explosion. We can pretty much assume that Godzilla's various atomic powers match or exceed that output. As far as hitting the Hulk goes, hitting a small target with his Atomic Breath would not be an issue, as Godzilla was able to hit the meteor containing Monster X while it was still in space with his breath in Final Wars. And even that fails, Godzilla possesses a nuclear pulse which would likely incinerate the Hulk.
And while it's true that Godzilla would meltdown after absorbing too much radiation, keep in mind that that's only held true for nuclear radiation, and not necessarily gamma radiation. If gamma radiation does work that way, though, the fight would end in a draw, as the Hulk would not survive the outcome. Also, it can be postulated that the energy Godzilla would expend during the fight against the Hulk would be enough to continually keep his radiation levels in check.
Overall, a good fight, but Godzilla would beat the Hulk in the end.