NVIDIA claims its latest chip is fives times faster than Tegra 2 overall, four times faster for web browsing, three times faster for graphics thanks to its 12-core GeForce GPU. This GPU can also handle 3D, which the Transformer Prime can then output to a bigger screen via HDMI.
In terms of CPU-intensive tasks, we're 'only' looking at a doubling of Tegra 2 performance. Nevertheless, it's a CPU comparison with Intel's Core 2 Duo T7200 processor that NVIDIA uses as evidence for its claim that Tegra 3 is the first "PC-class processor for truly mobile devices."
At the same time, Tegra 3 draws less power than its predecessor. This is largely thanks to a fifth "companion core" that kicks into gear for certain tasks, leaving the four more hungry cores switched off, as well as a smart 40nm process that employs two different classes of silicon -- one more suited to low-voltage activity, and one for the more energetic stuff. As a result, the Asus Transformer Prime is claimed to run 1080p video (which runs entirely off the single companion core) for a full twelve hours.
In terms of real-world impact, the Tegra 3 ought to allow game and app developer to incorporate all manner of visual wizardry into their products. The screenshot below shows how a game called Shadowgun benefits from realistic damage and water effects thanks to the faster processor.