It's very different. A fingerprint is only a unique identifier. Your genetic code is an infinite source of information about you and your entire family.
Can you imagine your health insurer or future employer being able to screen you for future health issues from a database because you got caught up in a bar brawl when you were 21? How about having your genetic information end up being used for bioweapons research because you pilfered an avocado?
Wanna lose your kids? Care to end up on a "watch list" because you have been identified as "high risk" from your genetic makup for some unwanted behavior? Try doing any of that with fingerprints.