I am actually not enamored with most of the Godzilla films. Most of them seem childish, silly, and stupid. The first is a classic, and there are a couple of other really good ones.
One I missed was the one from 2004 (?) which featured ALL the monsters, including the 1998 version of Godzilla. I would like to see that one.
That's Final Wars. If you don't enjoy the silliness, I don't think you'll enjoy that one either. It has a lame Matrix style "you are the one" type of plot with the main guy, mixed in with some shape-shifting aliens taking over the government, along with some MMA fighter or something, who only speaks English throughout, yet everyone understands him, and he understands them. To an English speaker, he's basically a reverse Chewbacca.
As you probably know, I enjoy "so bad it's good", and Japanese movies often hit the spot with me. Today I watched Godzilla Against Mechagodzilla, where Japan decided that the only way to defeat Godzilla was to spend 3 years making a clone cyborg Godzilla of their own, that immediately goes mental and starts destroying Japan, so they have to basically wait for its batteries to run out. Great stuff.