As everything is taking place on servers rather than your phone, Google isn't facing constraints on processing power or storage with Sound Search. It's combing through roughly 1,000 times as many songs, and is using a neural network four times larger. It also increased the number of dimensions (that is, details in the fingerprint) to reduce the amount of work, and doubled the density of those fingerprints (to increase the chances of a match). The result is song recognition that can search a much wider range of tunes and produce matches considerably sooner.
The company acknowledges that there's still work left. Its methods aren't good at picking up sound in particularly loud (or quiet) spaces, and it isn't as quick as it could be. This might not make you drop Shazam if you're already a regular user. This could, however, be just what you're looking for if you need to identify a catchy song and prefer Google's ecosystem.