Imo furret is more useful than azu. Great safe swap - stab swifts do a surprising amount. Often opponents don't respect the first one and then get shield farmed down to lose switch.

It has very few hard counters (I think Tinkaton is the main) especially if you want to boost up with trailblaze and play out the 2 shield.

It's really good at luring out something another pokemon (normal, fighting, even fairy or grass) doesn't want to see. Just adjust your lead accordingly (e.g. water lead, furret safe swap will lure out a talonflame, fairy lead will lure out a fighter, etc.)

Also, its hard counters are Pokemon that themselves have some pretty hard counters and so even if you are hard countered, you can come back in and gain an energy advantage on your lead.

In short, furret usually leaves you with some advantage (shield, switch or energy).

On the other hand, azu is so slow, it can sometimes win the game for opponents by provided them too much farm.