Both the Asus Eee Pad Transformer and Apple iPad 2 feature IPS displays. Aside from AMOLED, which is not yet available at these sizes affordably, this is the best type of display you'll find in mainstream consumer electronics devices. Apple deserves a round of applause for setting the bar for tablets this high by putting one in the original iPad.
IPS standard for in-plane switching, and it involves different crystal and electrode structures to standard LCD screens (usually based around TN, twisted nematic, tech if they're affordable). The results are superb viewing angles and great colour reproduction, no matter where you're looking at the screen from.
As the bar is set so high here, you probably wouldn't be able to tell much of a difference between the two displays without having them side-by-side, but the iPad 2 does offer better colour reproduction. Apple has clearly spent quite a while calibrating the second iPads' screens because it's still the display to beat.
Where the Asus Eee Pad Transformer does trump its rival though is in screen resolution. The iPad 2 has a 1024x768 pixel screen, designed to pack-in four times the pixels of an iPhone 3GS, where the Transformer takes a widescreen approach with a 1280x800-pixel panel. That's a massive 237,000 extra pixels on-screen in total.
The Transformer does have a slightly larger screen to spread these pixels out over, but the pixel density is still higher than the iPad - 149ppi against 126ppi (pixels per inch). This figure gives you a good suggestion of how sharp a screen will be. Both are obliterated by the ridiculous 329ppi of the iPhone 4, mind.
Touchscreen and Browsing
In a similar vein, both touchscreens are capacitive, highly responsive and multi-touch compatible. At this level of tech competence, the user experience relating to the touchscreen will be more dependent on the software than the hardware. And here the iPad wins, thanks to the sheer slickness of iOS. This is particularly noticeable when browsing the web, although both offer great surfing - and the Transformer is Adobe Flash compatible, where the iPad 2 is not. There are some workarounds available though, such as the Skyfire browser app, which acts as a middle man between Flash video and your iPad, enabling playback.
If web browsing is your main prospective tablet task, take into account that there's currently only a Wi-Fi version of the Eee Pad Transformer - with no 3G connectivity. A 3G-enabled version is on the way, but you can expect to pay a premium over the current version. It's likely to be up to £100 more expensive.