I can't speak for everyone, but I'll try to explain why he's my favorite anime/manga character of all time. I could write pages and pages about why this is the case, but I'll try and keep it short.
Before going any deeper, it's safe to say that Itachi is a masterfully written and likeable character, mainly because of the characteristics you mentioned. Sure, there are simillar characters to him in other works, but none quite exactly like him. He has a certain "something", certain attributes that make people hold him in high regard.
Personally, I found Itachi to be a very relatable character. I share a lot of his ideals, morals, and his way of thinking. So that's one reason why I hold a place for him closer than most other characters.
Additionally, if you look a little deeper, you'll find that Itachi is much more than just a character. There are many parallels and references between his life and Shinto mythology (namely the deities Izanagi and Susano'o). He's a symbol, in a very real sense.
But, as you implied, most of his "fanboys" utterly neglect who he was and what he stood for, in favor of trolling. That is indeed unfortunate.
Shinji? He really isn't in any way similar to Itachi.
Still an excellent character, though.
