IFilters are plugins that allow the Windows Indexing Service and the newer Windows Desktop Search to index different various file formats so that they become searchable. Without an appropriate IFilter, contents of a file cannot be indexed.
Both do the trick, of course, but your mileage may vary. Jie Li did a performance comparison between the two (Deb Haldar did the same for the 32 bit versions earlier) and found that the Foxit iFilter was about 5x faster than the Adobe version with his set of PDF documents. The Foxit iFilter now costs about $329 per dual core server, while the Adobe one is free. So you should consider what your environment contains and what you’d like to spend.
I would suggest trying both iFilters in a test environment that has a corpus of documents similar to your production environment (an exact copy would be best) and see which works better for you, then decide. Different document contents, a mix of languages, etc. can change the performance profiles of indexing, so you’d make a better decision based on testing with your own content.
Be sure to follow the installation instructions from start to finish, as there are a few “manual” steps required to update the registry on the server, register the document icon, and such, depending on which iFilter you choose.