I wouldn't compare him and Emery. Emery is a guy who has had many attempts at well resourced clubs and never been able to bring major success but competes for goals in the tier below (EL, top4 etc).
Inzaghi has led a team with negative net spend during his tenure, in financial crisis and utterly deconstructed under Zhang, to being the best team in Italy and probably one of the best teams in the world with players like Darmian, Calhanoglu, Mkhiytarian, Alexis who were considered washed up Prem rejects before they came to Inter.
He is probably pound for pound doing the best job in world football. With the resources of Pep? Inter would be winning trebles again.
His CV is too small and he's way too new to compare to Emery.
Pep and Klopp are far away because of their body of work.
Emery has managed many clubs and won multiple trophies and proved himself as an effective cup and league manager in varying situations. PSG is a poisoned chalice and Emery with much lesser control than Arteta, got way better results immediately in his short stint. Arteta took years to finish above 8th place in the PL despite huge financial outlay. It's a bit unfair to dismiss Emery on that front. He hasn't had a proper crack at a big club imo.
Inzaghi has had a great start to his managerial career and is doing a phenomenal job with Inter but you need to slow down here and wait for him to expand his body of work. If I was a big club owner, I'd definitely consider hiring him in 2024 for my club.
I'll give you a Footballer analogy. If Pep and Klopp are 32 year old legends who compete for B D ors almost every year and Emery is a 28 year old player who has won the lot in multiple clubs despite his unfortunate stint at a club then Inzaghi is a 23 year old player with World Class potential who has carried his team to a CL final recently despite playing in a relatively average team.
Let the kid consistently perform for a few years before you put him in the same bracket as some of these veterans/experienced superstars.
I hope I explained my point well. Feel free to correct me if I am wrong.