This may sound like something incredible to believe - I mean not only is new iPad just as fast in general as the iPad 2, because it has the same old dual core 1 Ghz CPU as last year's iPad, but now it's highly hyped GPU gives it slower performance as well? How is that possible?
The short answer is: retina resolution. The old iPad GPU was very powerful, and now the new GPU in the new iPad 2 twice as powerful. The problem is it has to push 4 times as many pixels as as the old GPU. So it's twice as fast, but has to do 4 times the work. That pretty much guarantees that the new iPad is slower for all apps and games that will use the Retina resolution. And since all developers will want to do that, that means this will start to become obvious very soon for the owners of the new iPad as well.
Anandtech's view on this:
Pay particular attention to how, at 1024 x 768, performance doubles compared to the iPad 2 but at 2048 x 1536 performance can drop to well below what the iPad 2 was able to deliver at 10 x 7. It's because of this drop in performance at the iPad's native resolution that we won't see many (if any at all), visually taxing games run at anywhere near 2048 x 1536.
Another surprise that we notice is that the new iPad is just as fast as a Transformer Prime in terms of GPU performance. This is hardly the "4x faster" they promised at their launch event. Just to be clear, I do think the new GPU is faster than Tegra 3's GPU. When the chip itself is twice as big as Tegra 3, it's no surprise there. That's also one of the reasons why it needs almost twice the battery as a Transformer Prime.
However, what users want to know, besides some mental battles over which GPU is theoretically the fastest, is how fast their actual device is - and if it's faster than the older iPad. Again, the answer to that is: no, it isn't. The retina resolution ensures that the new iPad is at best just as fast in GPU performance as a Transformer Prime, or any other Tegra 3 powered Android tablet.
It's also important to remember that although there's a lot of talk about the GPU's lately, the CPU is still the most important part of a chip, performance wise. The CPU is the one that handles most apps in general, and if you want a better/faster experience - you'll need a faster CPU. The new iPad uses the same CPU as iPad 2, so browsing and most apps will work only as fast as on the iPad 2, and perhaps even slightly slower if they are affected by the new resolution as well.