If Script Editor is the hamburger of AppleScript, Xcode is the two-pound steak. It's fatter, heavier, and more tender in the middle than the humble Script Editor.
In all seriousness, though, Xcode is a power user's dream compared to Script Editor. Although most people use Xcode for writing full-fledged programs (Section 15.2.1), there's nothing to keep you from using Xcode to write and debug your scripts. In fact, Xcode has a number of features that simply aren't available in Script Editor—features that can save you time, trouble, and tons of repetitive debugging.
First, however, you have to install Xcode.
If you're a feature fiend, be sure to check out third-party AppleScript editors like Smile and Script Debugger. Those programs include even more debugging features than Xcode, as detailed on Sidebar 2.6.
Xcode is part of a powerful package for programmers (say that five times fast). Depending on whom you ask, this package is known as either the Developer Tools or the Xcode Tools. Either way, you have to install these tools to use Xcode.