Biggest difference is when the phone reads app data that's stored on the SD card. Honestly, a class 6 card is by no means fast when compared to data on the internal memory. Having said that, IMO a class 6 card is about 300% faster than a class 2. Never used a class 4 card, but I'd guess it would be somewhere in the middle lol.
Since most apps will store data of some sort on the card, you will see an overall increase in the system speed using a class 6. The biggest difference will be any app (or while in the settings) that reads/writes pictures from the card. Small files (example Robodefense config

) isn't that big of an increase.
Now please...this is all from MY EXPERIENCE. Of course HTC and Sprint haven't and probably won't ever comment on the differences.