While I've never seen any of the old Godzilla movies, I suspect that this cartoon is simply not for the same crowd. It is, however, for people who watch cartoons. I should say that I enjoyed the most recent Godzilla movie. It wasn't great, but it was fun. In some ways this cartoon is better.
The cartoon follows the movie plot-wise, and has all the main characters, though the spotlight has shifted somewhat. Nick himself is a much cooler character this time around, as befitting his position as an action cartoon hero. Major Hicks, Audrey Timmonds and Victor "Animal" Palotti show up infrequently, and for some reason French spy Phillipe Roche is almost completely absent. Dr. Mendel Craven and Dr. Elsie Chapman and now main characters, along with two newcomers who balance out Team HEAT quit nicely.
Maybe it's just me, but I miss the old heroes. These days too many cartoons, movies and TV series are just about idiots acting stupid, there's not many characters we can look up to anymore. Fortunately, team HEAT are all about heroics, Nick is always leaping into action and Monique is quite the professional. That's not to say that Godzilla doesn't have any comic relief, we do get to laugh at characters and running gags (love those running gags! Poor N.I.G.E.L. !). But the comedy is less about stupidity and more about personality than some things out there.
The series does try to have some scientific basis behind it's plots, making the stories easier to accept and more enjoyable to follow as there is some level of logic involved (though that's not to say you're going to actually believe any of this stuff could happen, it's not quite that convincing). The cartoon combines the human element of the newer movie with the giant monster battles of the older movies in a typical "strange new adventure everyday" cartoon format. While I'm sure many people like myself would have appreciated a more substantial, running storyline rather than the one-shots presented, the format is probably more suitable for younger audiences and infrequent watching, so you can just enjoy it as you see it.
Overall, this is one one of my current faves. Watch it if you are still young at heart and enjoy a little light action and humor.