If you watched How To Train Your Dragon 2 you notice that during the end of How To Train Your Dragon 2. Toothless turn blue by challenging the Bewilderbeast. Like how Godzilla's Spikes turn Blue. Here is couple reason why Toothless is Godzilla.
Godzilla and toothless is the Alpha or King
After the battle of Toothless and the Bewiderbeast. Toothless is the new Alpha and the Alpha protects them all. Godzilla is the king of the monsters.
Godzilla and Toothless help people.
Another Reason is that Toothless is friends with Hiccup. Toothless Protects the people of Berk. He also protected Hiccup twice in the franchise. In the new Godzilla movie, Godzilla is swimming by Navy Ships like is nothing. Listing to the Soldiers, Godzilla is protecting the bus on the golden gate bridge. Saving Aaron Taylor Johnson from the female Muto.
one reason to make this Theory kinda right is, that Toothless evolve. Just like how we think Apes evolve into Humans. During Httyd time period, it would be long ago. Toothless started to lose wings and grow bigger and started to walk on two legs and started swimming.