I had to ask myself the same question recently. The tipping point that made me go with Advanced was the Script Debugger and Data Viewer. I'm not good enough at troubleshooting to go without it.
I can't answer about the standalone on different platforms.
+1 to what Matthew said.
FMP Advanced also has the database design report which is very helpful.
The FMP Advanced purchase includes installers for both OS X and Windows. FMP files will work on both platforms (with some adjustment to field sizes due to font differences and a small number of script step exceptions that are platform specific). A Windows runtime must be created on a Windows system but that can be a Mac with bootcamp plus a Windows license.
So would one licence cover using both downloads?
I never try to modify a database without using Advanced.
When you purchase Advanced, the dowload page allows you to download installers for both systems. Download and make multiple back up copies of each installer. (Keep at least one copy of each on removable media, a cloud storage location, or a second computer so that if your current computer suffers a catastrophe, you can install on a new computer without having to ask FileMaker Inc. for a new installer file.)