It was just as simple as it sounds, just make sure to move your gamer profile over to a memory unit before you start the setup on the other console. Then, insert the memory unit in the other console before you turn it on. Then, go through the setup, and eventually it will tell you that gamer profiles already exist on this console (instead of having you go through the whole process to create one or to recover one). After you select your profile, it will say that an update is available over Xbox Live. The download was fairly large, but when it was finished, I had noticed all of my XBLA games were now on the new hard drive. However, it did not download any additional content for those games, you have to transfer those over yourself (Uno decks for example, I had to move those over myself).
Another thing I noticed about the new hardware, which may or may not be of any significance, is while registering the console to use on the campus network, I noticed the first half of the MAC address was slightly different (the half used to identify a manufacturer, etc). So, there may be a new type of NIC inside there.
EDIT: As an update to my postings for tonight, after I actually went to look at those arcade games, they are actually only just the trial versions. They must have been preloaded onto the hard drive. Oh well, just means I'll have to redownload a bunch of them over again. I guess I originally should have taken a closer look and seen that not all of the games I originally had were there. At least for the trial versions that are already on the hard drive all I have to do is select "unlock full game" again, it knows that I owned it before and doesn't charge for it. All I can say is hooray for the download history list in account management, made it very nice to download my TV shows again too.