The chosen container format for ASDF is HDF5. The Hierarchical Data Format version 5 is a quasi standard format for binary data with a large amount of tools and support available. This format has also shown promise for dealing with large datasets in other applications.
ASDF delegates the allowed compression, chunking, checksumming, etc. settings to the HDF5 definition. Best to not use use custom filters that are not shipping with the HDF5 library as it will severely hurt exchangeability and possibly future safety. The HDF5 group puts a lot of emphasis on backwards compatibility.