My understanding of the difference is as follows:
Crystallizing encapsulants are designed to dry into hard particles that "trap" or encase soil particles, making it easy to remove the soil afterward through vacuuming. The ideal crystallizing encapsulant is almost entirely vacuumed away within a short time after the cleaning process is done. Good crystallizing encaps should shatter and make brittle shards if left in a dish to dry out overnight. Often the crystal structure of the chemical will give the carpet a brighter, fresher look because of the way it reflects light back to the eye, so even though a lot of the soil is still there immediately after cleaning, the carpet looks cleaner.
Filming encapsulants are designed to encase the carpet fibers themselves, preventing the soils from attaching strongly to the fibers and dislodging soils during the application process. Filming encapsulants are designed to peel off in "strips" or "sheets" over multiple vacuumings, allowing the film to continue soil-bonding prevention for an extended period of time. Filming encaps will form less of a shard and more of a slick or even slightly sticky residue if left in a dish to dry overnight.
Either process will require regular vacuuming from the customer to produce the best results.
I'm a fan of crystallizing encaps because I'd rather vacuum than do laundry.