While USB 3.0 may theoretically have a higher bandwidth than SATA III, converting from USB to SATA protocol actually decreases the write speeds, which are critical for writing large video files. For example, while writing to a hard drive with a SATA connection (How internal hard drives are traditionally connected), you may get 70 MB/s. With USB 3.0, you may only get 30 MB/s. (I'm just pulling some benchmarked numbers I've seen comparing SATA III and USB 3.0).
The moral of the story is, you get more space and performance for your dollar if you go with an internal hard drive which you connect via SATA than if you went with an external hard drive that connects with USB 3.0. I also recommend you get a hard drive with a 1 TB+ capacity. Video files stack up quickly!
I personally record 1080p/30fps gameplay with one of these (http://www.newegg.com/Product/Product.aspx?Item=N82E16822236339) and have never encountered any bandwidth issues.
Is there a particular reason you went with External vs Internal?