Both the Dyson Airwrap and the Shark FlexStyle use a technology called the Coanda effect. This is when flowing air or water sticks to a curved surface and creates lift. Basically, the tools direct flowing air at your hair, and the hair follows the lead, wrapping itself around the tool ready for styling. Because it uses this method, rather than heat, it’s deemed better for your luscious locks.
The consensus is that this method feels more powerful on the Airwrap, so the final result feels more salon-worthy with minimal frizz.
The Airwrap barrels also create better curls as they are longer than the FlexStyle, so you can curl higher on your head, giving your hair more volume and bounce.
As for how long your styled hair will last, the FlexStyle and Airwrap are pretty much on par with each other - expect your curls (or straight hair) to stick around for a couple of days, depending on your hair type that is.
One category where the Dyson Airwrap comes out ahead is volume - no, not hair volume. The actual sound your hair styler will make. The FlexStyle is much louder, and while that may not be a dealbreaker for most, it is worth noting that Dyson-styled waves will not be as noisy.
And for when you step out of the shower and need to dry your hair - it’s the Shark FlexStyle that comes out on top. The Dyson Airwrap isn’t designed to replace your hair dryer, rather it prefers your hair damp, ready to style into curls or to straighten it, depending on which attachment you choose. The Shark FlexStyle is suitable for simply drying your hair though, if you don't feel like styling it.