The short answer
Both listen for crying and respond with motion and sound, but they're built on different ideas. The SNOO runs all night at a gentle baseline and escalates through four more levels as it detects fussing, with your baby clipped into its sack. The Eluma Nest stays still until it hears crying, then cycles through rocking, vibration and sound, with no swaddle system and no app.
The SNOO is the more refined soother, and its app, weaning mode and sleep logging are genuinely useful. The Eluma Nest wins on price (around £200 against £1,395), on UK certification (Graco lists EN 1130:2019), and on sitting more comfortably with Lullaby Trust advice, since nothing holds your baby in place.
My call: the Eluma Nest for almost everyone. Choose the SNOO only if you can rent one, you're comfortable with the clip-in sack, and the most sophisticated soothing is worth the premium to you.