Many hate him and think he is one of the worst managers out there, some love him (not too many though) and unconditionally appreciate every choice he makes both on and off the pitch. That's why is really hard to understand Roberto Mancini's true value, especially in his last year and a half in which he had to take charge of the sinking ship Inter was when Thoir and Moratti finally decided to fire Mazzarri. He had the courage to take a high-risk job, especially because of the incredible success he had in his first stint managing the Nerazzurri.
Taking over another manager mid-season is always a very hard task, tactically and mentally. No matter what you do, you will always be compared to the one who sat in your spot before you arrived. The Italian media in particular are maestros at criticizing harshly and (often) unfairly the manager's job and they often take pride when they are able to point out mistakes or bad decisions by one of them. Mancini hates this behavior and he never hid his feelings about it but he loves Italian football so much that it was almost impossible for him to turn down the offer, most importantly because it was Inter that wanted him. He is an emotional person and that's why it's so hard for him to work with serenity in a high-pressure environment like Inter. He always wears his heart on his sleeves and he doesn't fear making bold statements in front of cameras. The Sarri incident is a great example of this trait of his personality. When he appeared to make the post-match interview he looked really shook by what just happened on the field and it wasn't a premeditated act to somehow discredit the Napoli manager. He wasn't being a snitch, he was being real, he was being himself.
Mancini is not a top-class manager. I wouldn't put him in the same conversation with Guardiola, Ancelotti, Mourinho, and even Allegri who proved to be much better than most people thought before taking over the managing role at Juventus. He doesn't have Pep's tactical brilliance or Mou's positive arrogance and he probably never will be on their level. But is not that bad, and I think, to answer the question in the title, that he is good enough for Inter. For this rebuilding version of Inter, at least. With a squad that is far from being one of the best in Europe quality-wise, having one of the best manager on the bench now could prevent Inter from having him in the future when, with a better roster, the team could go back winning trophies again.
Mancini has done everything I expected from him in the past one and a half years. He finished a disastrous season without caring too much about the results in order to put more focus on giving the team his personal tactical mark. It worked, and the rather impressive start of the 15/16 season is evidence of the good work Mancio has done with the team. The quality of the roster surely benefited from the on point transfer market made by the club (shout out to Ausilio for his incredible work with so little money to be spent) which was aimed to bring the best fit into a squad that had so many void to fill. Mancini wanted to reinforce his team acquiring one key player for every department, and it worked: Miranda helped the defense became solid again, Kondogbia has huge upside and already showed his incredible ability at disrupting the opponent's play and help his team start the offensive maneuver, and Perisic, after a slow start, finally found his rhythm and started to be extremely dangerous every time he had the ball. The project Mancio has in mind for Inter is still raw, but if you look at his decisions in perspective, the team took the right path to became relevant again, pairing experienced players with younger ones. Of course, he also made some mistakes while trying to figure out which players could be the best fit in his project. Melo, Jovetic and Ljajic are all good players on paper, but they never found their niche and they ended up doing more harm than good to the team's chemistry and quality.
I'm not a fan of Mancini and as I already said, there are higher quality and better prepared managers around. He is what Inter needs at the moment; he is capable of building a good team and has great eye for young players, an underrated quality that is very important in rebuilding times. I like what he has done with the team so far but I also expect the management to have the balls to give the keys of the team to a top-class manager when things get serious again.