I wouldn't assume a faulty module unless I had a very good reason to, especially if they are new. I assume you tried it more than once, i.e. unplug the cable to power it off, reseat it, then try again? I wouldn't hot-swap the modules, disconnect the power (USB) first.
If you're not clear on AT mode vs. API mode, then you need to do some reading. But briefly, in AT mode, two XBees just pass serial data between each other. Think of it as a wireless modem set-up. What goes in the TX pin on one, comes out the RX pin on the other, and vice versa. I believe that this is how a lot of people use the S1 modules. To set this up with S2 modules, one needs the AT Coordinator firmware loaded, and the other needs AT Router firmware. Then three AT commands need to be sent to each module to set its destination address to be the other module (ATDH, ATDL, ATWR). The address is a 64-bit number (16 hex digits) that is on the bottom of the module, and will start with 0013A200.
API mode is more structured, and communicating with the XBee is more demanding from a software standpoint, the sketch has to use well-defined frames to communicate with the XBee. There are some very good libraries out there that help tremendously with API mode. If you haven't already, download the product manual
from the Digi web site, as this has all the technical details needed to make XBees jump through hoops. I also highly
recommend Robert Faludi's book, Building Wireless Sensor Networks.
So, while easier to set up, AT mode in my mind is actually more difficult in one sense, in that we basically have to deal with a continuous stream of characters, and create our own protocol to send structured data from "A" to "B". If we're not careful to cover all the bases, it will be more error-prone as well. I don't recommend that a person new to XBees should jump right into API mode, although I think that is almost always the better solution.
My recommendations for you:
1. Start with AT mode, set the two XBees up to "chat" back and forth as described above. This can be done with two computers or with two terminal programs running on one computer.
2. Get your project with the pot and servo working on a single Uno. I would hope that you've already done this, and are not attempting to eat the whole elephant in a single bite.
3. Now introduce the second Uno, and devise a way to send and receive the data using AT mode. Send data on some fixed interval. Start slow, maybe once a second, maybe even slower. Once that works, speed it up to every 100ms.
4. Lather, rinse, repeat with API mode
XBees, S1 or S2, are fairly complex little beasts. The product manual for the S2 is about 150 pages, and even that for the S1 is about 70 (S1 also has API mode). Nevertheless, they work very well, will do a lot for you, and they aren't hard to use if you will take the time to understand them first. For my money, the S2 is a better deal. It has mesh networking which works really well if you add more modules, the transmitter and receiver have slightly better specs, and it actually costs a couple bucks less when bought direct from Digi (which is the best price I've found). Hope you have fun and enjoy learning about these very cool and powerful modules. Let us know how it goes!