Yes in general he transformed the playing style of the club and was able to achieve some performances/streaks. But that is more an indication of good coaching (most of the time). The question is his ability to be a top-class manager for a club wanting to compete at the very top end.
Sure, that question is still to be answered, but by all accounts he looks to be on the right path. As you mentioned- the only people really keeping him out of the top 4 are some of the most experienced and excellent coaches in world football. Last season, he more than held his own against them, and he has the benefit of youth to learn from all of these men. He's shown that while still possessing a very stubborn streak, he is not afraid to change when things are not going to plan.
Also, I think that he has matched Liverpool's expectations season after season. When he joined, they were mired in midtable and looked destined to spend at least 5 years there. He took them back into the CL in 3, when he had a plan to do so in 4, all without the sort of backing that other managers have had.
To be fair, the European pedigree and world wide appeal of Liverpool and Porto cannot be directly compared; even since the success Mourinho had with them. Mourinho was a talented manager who became bigger than the club he first won with...for Rodgers, the club and its expectations is probably a step too far, too soon.
Depends on the viewpoint, IMO. Porto are the Portuguese equivalent of Liverpool, so I wouldn't say that Mourinho became bigger than them in that respect- more a case of overall European ability and potential for success. Liverpool are actually a few pegs down currently, despite their steeped history. Rodgers matches that- they're still a young team, with the expectations to match.