I remember very well when Steve Jobs said that they believe that products should be more than just a list of specs, but even though he always tried to downplay the specs, they kept coming up in their keynotes, and they were bragging with them. But usually, there's also something special along the list of specs. This time, I couldn't really see it.
The iPad 3 brought the same dual core CPU, perhaps overclocked slightly, most likely at 1.2 Ghz, if at all. Then the GPU received a pretty big upgrade, saying it's 4x faster than Tegra 3, but with the 2048×1536 resolution it also received, and also only using LPDDR2 memory, the real world performance increase should be a lot smaller.
How will Android tablets perform compared to it? For starters, the iPad 3 resolution is only this big because Apple had no choice but to double the resolution in order to make it easy for developers to scale up their apps. But other than that, 1080p movies will look no better than on 1920×1200 Android tablets. In fact, it will look just as letterboxed as they've always been because of the 4:3 display ratio. Plus, Apple may get to say they have the biggest resolution on a mobile device right now, but Samsung will beat it handily with a 2560×1600 resolution tablet very soon.
In terms of raw performance, the CPU is still only Cortex A9, and it should lose out in a competition between a quad core Cortex A9 chip like the Tegra 3, and even more so compared to a dual core Krait or a dual core Cortex A15 CPU. In terms of GPU, it's pushing 4x as many pixels, while the GPU only gets increased by 2x. This means the GPU performance should even be slower than an iPad 2. But this also depends on whether they increased the clock speed or not for the GPU's. If they did, then perhaps the performance is about as good as the iPad 2, or slightly better, but not 4x better.
Overall, the iPad 3 doesn't bring anything completely unexpected, comes almost 1 cm thicker, so I doubt it will impress too many people, at least those who know their tech.