It depends on what phones you might see yourself using in the future. If you plan on sticking with Android devices, backing your contacts up with your Google account is definitely the way to go. But if you think you might switch to an iPhone, Windows Phone, Blackberry, or dumbphone at some point in the future, using Backup Assistant will make things a bit easier. There are ways to get your contacts from Google onto all of those devices, but Backup Assistant will be simpler and will provide more options.
If you're not sure what phones you'll use in the future, you could always use Google for now, and then if you think you'll be moving to a non-Android device, do a quick backup with Backup Assistant. Or you could just use both concurrently.