I've experienced this under Firefox, and on hardware that has no excuse for breaking a sweat on any webpage. It's usually pages where there are a large number of animated GIFs (e.g. [1]) Once all the GIFs are loaded and complete one animation cycle, everything's fine.
Are you sure you're not referring to animated GIFs? The slow FPS rate occurs as they load, and is contained to the GIF itself. Surely a static GIF would not reduce your browser FPS.
Don't be so sure it's a loading issue. I very often have animated gifs play very laggily the first time they run, even when they were already fully downloaded. And across multiple browsers I have seen issues playing gifs smoothly when there is anything else in the browser using CPU.
