Take a look at our documentation on the differences between Binary/Pattern and Trie.
We match our API versions to our data file versions - so if your API version starts with 3.2, use V3.2 data files. If it starts with 3.1, use V3.1.
Most of our up-to-date APIs use V3.2 data files, with the exception of Node.js and pure PHP (not the C wrapper). If you are using one of these technologies, and older API, or an older CMS (such as Kentico 8), you may have to use V3.1 data files.
Unfortunately we no longer release updated V2 data files. If you are still using version 2 of our API, we strongly recommend you upgrade in order to stay updated. Check the documentation for your technology for instructions on upgrading to version 3.