I actually enjoyed the soundtrack for Godzilla, it fit the movie extremely well. I've also seen some of the fan videos on youtube, and think that the Ifukube's music is really out of place with the new film. Just doesn't fit at all.
As far as the soundtrack being unmemorable, I do agree. While it's good music, it's nothing that people will remember. I also think the same can be said for the music in the Dark Knight trilogy, especially for Batman Begins. While I thought the music for the trilogy was very good, it's nothing will make me personally remember it too much.
On the other hand, Danny Elfman's score for the original Batman was amazing and many people always remember. Sometimes my wife and I go to symphony concerts at my university and every now and then Elfman's Batman score is played. Love it every time that happens!

I think it would've been incredible if they had Elfman score Godzilla instead of Desplat, but that's okay it is what it is.
I hope for Godzilla 2 Desplat steps up and creates something amazing and memorable, otherwise I just hope they replace him. There are plenty of amazing composers out there.