So, I downloaded the 1.13 mod, and I want to change a few things in the INI file. But which INI file should I change? There is one JA2_Options.ini in the Data folder, and one in the Data-1.13 folder. And these are quite different in their content.

So, which one do I modify? Which one will the game access and use?

The 1.13 mod uses data in the Data-1.13 folder. To make your life easier, use the 'INI Editor.exe' inside your installation folder, but be sure to make backups, in case you go too far or bork things up.

Short answer is the Data-1.13\JA2_Options.ini

Longer answer is that it depends on the VFS you use. Assuming you use the 1.13 VFS, it will first check in the Profiles\UserProfile_JA2113 folder and then in the Data-1.13 folder, and failing to find a JA2_Options.ini in either it will look in the Data folder. So you can always copy your JA2_Options.ini file to the profile folder and modify it there, thus keeping the default in case you need it.

Should you have more questions, feel free to ask.