Andy:
Browser in a misnomer.
Both are loaded on your machine. However, whenever you start the "browser-based" version it checks to see if there is a revised/updated/fixed version of the the one you have. If so, it is downloaded and then the TWS opens.
If you search here at ET you'll see that a number of the IB stalwarts complain about "beta-testing" new versions of the TWS without being told they are beta-testing. IB actually does produce a beta version, but you must select it and download it. However, many feel every release is a beta.
You'll notice that the Browser version generally has a higher version number than the downloadable. If you use the "browser-based" TWS you are an early user of the latest version of the TWS. If you use the downloaded version, you are a later adapter of the latest version. By using the downloaded version you can be prepared for the latest "enhancements". Using the browser version is more exciting, especially if IB has changed the defaults on something and you don't realize there has been an update.
I am a long-time IB customer. I stick with the downloaded version.
Jack