Although the iPhone 4S looks like it'll slip right into your old iPhone case, it turns out there's one important difference: Apple unexpectedly moved the light sensor on the new phone slightly to the left. If your old case covers the front of the phone with a window for the earpiece, camera, and light sensor, it might not line up correctly on the 4S and the sensor could get covered. This makes the phone turn the screen brightness down because it thinks it's in a dark environment, so if your new screen is dim, check to see if the case is the culprit.
Of course, there's a lot of other new stuff under that familiar exterior, and it looks like one of the biggest unexpected upgrades is the ability to get location data from Russian GLONASS satellites in addition to GPS. The capability most likely comes from the less unexpected Qualcomm MDM6600 chipset that was confirmed by Fixit to provide the iPhone 4S's dual-mode CDMA / GSM compability — lots of other phones like the and Bionic also support GLONASS and use the same chip. This should make the location tracking a bit snappier than the iPhone4 — anyone out there notice a difference?