Ultimate showdown of all time

Having just watched Godzilla: Final Wars, I am left with many questions. Many, many questions, of which I will receive no answers.

However there is one answer I will definitely never receive, which upsets me.

If Godzilla fought Superman, who would win?

I'm trying to imagine it, and it is AWESOME, but I can't picture who wins. Let's try to reason this out. First, the ground rules

1. Godzilla is moving to attack Metropolis, but not there yet, so the fight is happening in a relatively sparse area, but with enough debris around to make it interesting. This means Superman HAS to fight him (to protect the city) but Godzilla can't get an unfair advantage by inadvertently threatening people Superman cares for, thus distracting him (E.G. Lois Lane is in danger... again)
2. Godzilla is pissed at Superman and trying to kill him, rather then just ignoring him and moving on.
3. There are no reinforcements on either side.
4. The story is being written by a neutral party, so no vested interest from either DC or Toho.

GODZILLA:

PROS:
- Enormous Strength. As strong as Superman is, I think current presentation of the man of Steel (rather then the bullshit "I'll spin the earth backwards and reverse time" thing) shows him as incredibly strong, but not Godzilla strong. I would go on record that I think Godzilla is stronger then Superman, and could he get a good grip on him it is entirely possible Godzilla has the strength to crush him to death.
- Radioactive breath. While Superman is probably agile to avoid this while flying, at least once this could be sprung on him as a surprise.
- Immense toughness. Godzilla is ridiculously tough, easily tougher then any other villain Superman has faced.

CONS:
- Slow. While his large gait means Godzilla can move pretty fast, Godzilla would not be capable of the kind of rapid self correcting swing needed to swat a human-sized target in mid air while it's flying. It would be like a human trying to hit a fly. Sure some people can catch them, but it's as much luck as it is skill, and you can swing all day without connecting.
- Large target(s). Superman could never miss Godzilla. He's friggin' massive. More importantly, let's assume that Godzilla, like is the case for all animals ever, has relatively sensitive eyes. Those alone are larger then a human, and as such easy targets for Supe's.
- No Kryptonite. That seems to be the only way to beat Superman these days.

SUPERMAN:

PROS:
- Strength. As I said, I don't think Superman is as strong as Godzilla, that said, he IS very strong. He could easily start using abandoned tanks (or equivalent weigh objects) as projectiles by flinging the damn things at Godzilla, who would have a hard time dodging them.
- Speed. Superman is far, far faster then Godzilla. Godzilla would have a genuinely tough time hitting a flying Superman, either with swinging fists, tail, or radioactive breath.
- Heat Vision. Let me start off by saying I do not believe that Superman's heat vision could hurt Godzilla traditionally. However, a blast of that to the eyes would slow ANY giant Monster down.

CONS:
- Not strong enough. Superman is strong and with a myriad of offensive weapons at his disposal. I do not believe either any of them, or he himself, is powerful enough to take down Godzilla. Hell, I don't even think the Hulk, jumping at full strength at Godzilla's head, punching at full strength on the way through, could knock Godzilla over, let alone Superman.
- Not enough leverage. It's shown in plenty of Godzilla movies the most damaging way to hit Godzilla is to throw him around or knock him down. I honestly don't believe Superman could pull that off. The only way I could see that working is if he, in a matter of seconds, flew past at the same angle and hit Godzilla over and over again on the way past. However, that opens him up to a Radioactive breathing to the face.


Y'see, this is my problem. In the vision I paint above, Superman cannot really hurt Godzilla, while Godzilla cannot hit Superman enough to really hurt him. A full blown stalemate, which is as satisfying as a carelessly abandoned blowjob.