The Google Experience branding is Google's attempt to stop the fragmentation problem. All Google Experience Phones will be running the same Android kernel which will help ensure compatibility with apps and features. The HTC Dream (G1) and Magic (MyTouch) are both Google Experience phones, but the Hero and Tattoo (and any other with the SenseUI) have a modified kernel. Basically, with a Google Experience Phone, that list of features in the link that Ticho gave are guarenteed to be on the device. If the device doesn't support all those features, Google wont let the manufacturer brand it as a Google Experience Phone.
Currently, I've only noticed a few big things the Hero is lacking. One is the standard speech recognizer (used for Voice Recognition). Another is a STT library, but that can be fixed by installing the extended library in the Market.
Hero users wont be missing anything from 1.6 if HTC decides to skip it and go straight to 2.0. Anything that would be added from 1.6 will be included with their 2.0 update. Because the Hero is not a Google Experience phone though, it's hard to know for sure which featurs will make it to the device and which wont.