I own both an iPad 1 and iPad 2 - the iPad 2 is faster - but for most current Apps, unless you were doing timing tests you wouldn't notice too much. For Example loading lego harry potter on the iPad 2 was maybe twice as fast as the iPad 1 but the iPad 1's load time was acceptable waiting time.
The other place that has improved is the graphics - just look up any 3d game that has optimized for the iPad 2.
As you can tell it is mainly gaming that benefits from the speed/graphics.
The reason I got the iPad 2 is I wanted to be able to Skype and Facetime without having to lug an entire computer just to do that. (Yes the iPhone can do it too) Don't bother with Pictures as the camera is very poor but for video and video chat it works fine.
The iPad 1 is still a great value but as newer OSes come out, Apple tends to drop support for older devices so you may not be able to upgrade to the latest and greatest with the older models after some time. (Good example is iPhone 3G - could upgrade to iOS 4 but didn't get multi-tasking, and some other key features. Won't be supported with iOS 5 - currently 2 models back, 3GS - some things in iOS 5 won't run allegedly, and that is just 1 model back, etc etc) That being all said - as MymacROX stated - if iPad follows the same release schedule - then iPad 1 still has some legs before it becomes 2 Generations back.