One source would be the Hydrogen Audio forums where there are regular scientific comparisons - PSNR etc. instead of blind listening tests - between various encoders and formats. Apple's AAC encoder consistently comes out well above anything MP3, best of all the AAC encoders, and up at the absolute top together with Opus which produces a bit better results per same bitrate.
> Does it matter that much? From what I know, it just about properly programming a math spec, with some tricks but I wonder if that makes that much of a difference.
It does matter a lot and the difference can be staggering. Producing the audio bitstream is a case of both effectively analyzing the original input and programmatically expressing the waveform as correctly and as efficiently possible. Two excellent examples: the old MP3 encoder Xing, which compared to LAME produces very poor material even at higher bitrates, and one of the earliest open-source AAC encoders, FAAC, which also renders a very poor product. A lot of "early adopters" got bitten by FAAC and many of them still stubbornly cling to the misunderstanding that AAC is a worse format than MP3.