Regigigas is, as mentioned above, multi-continent level in both AP and durability, whilst Kratos is only large continent level. This means that Kratos would have to deal lots of blows to Regi to damage him while a few full power hits of Regi would be enough to incapacitate Kratos. On the other side Kratos is more agile since he is smaller. But because of speed being equalized it won't make that much of a difference. Kratos has more fighting experience though.
Let's look at their other abilities. Both have some forms of elemental manipulation. Kratos can only use them for attacks while Regi can also use this to create new golems. It should be noted that the golems he creates are multi-continent level in AP and durability, while also being faster than Regigigas himself, namely their in the same speed tier as Kratos. Kratos on the other side has a variety of hax at his this disposal, such as petrification, soul manipulation, create a shadow clone and life energy absorption (Time hax are prohibited by the rules of this thread). I have only seen parts of the game but those abilities seem to be less effective on powerful enemies (don't know about the shadow clone though), so it is questionable if they work on Regigigas.
Is there prep time? If there is, it is clearly Regis win. No matter how effective Kratos hax might be on Regi, against an army of multi-continent golems he stands no chance.
If Regi is mostly unharmed by Kratos hax or is able to create a new golem before Kratos can significantly damage him, it is very likely Regis win as well. If things are the other way round it would most likely mean Kratos victory.
To sum it all up, I'm leaning slightly more towards Regigigas due to better offensive and defensive stats. Therefore my vote goes to Regigigas. Should someone bring information on or explain credibly how Kratos can affect Regi with his hax, I'll most likely change my vote to Kratos.