Okay, I decided to go back to 12.04.
Something screwed up with Jockey, it says that "Ubuntu has encountered an internal error" whenever I try to open the Additional Drivers.
sudo aptitude install fglrx didn't make my computer explode, but it didn't improve my MC framerate.
The error occurs in both OpenJDK, and the Sun JRE (which is officially suggested by the Minecraft website.)
When running Minecraft via the terminal, I get a TON of "WARNING: Can't keep up! Did the system time change, or is the server overloaded?" messages, even though the system time DIDN'T change, and the computer is most definitely NOT overloaded.