I couldn't really think of any significance until now, when I realized that this isn't an isolated incident. The parallelism should be just as obvious for Shinji's fight against Shamshel... if it's translated the right way. I didn't actually realize it until Rebuild, but Kensuke intended for his statement "Being hit like that must have really messed him up" to refer to Shamshel's attack a couple of seconds before he said it, but Toji misinterpreted him and snapped back "Shut up!", assuming Kensuke was referring to when Toji punched Shinji. The line has a double meaning that works equally well in both contexts. I saw the dub of the episode first, and unfortunately ADV messed up the ambiguity by having Kensuke specifically say something along the lines of "That punch you gave him must have really messed him up".
It should be obvious at this point that Shinji's interaction with humans is supposed to be mirrored in his interaction with the Angels. The parallelisms get a bit less clear after the first two, but I don't think the concept was abandoned. One of the few things Matt Greenfield got right was the double meaning of Ritsuko's (or was it Misato's?) statement that they learned a lot about "the enemy" after Shinji and Asuka's fight with Gaghiel. Again, the Angel battle directly corresponded to Shinji's interaction with Asuka during the fight.
But wait! There was another fight between those two! What about Ramiel? This one isn't as obvious, and I wouldn't have thought to look for it if I... hadn't... thought to... look for it. This fight is clearly about his interaction with Rei, but is there a specific parallelism there?
This is my guess: Shinji's first attempt to socialize with Rei was a complete "miss". When he was in Rei's apartment she pretty much ignored him, and when he badmouthed Gendo he got slapped IN THE FACE. His first attack on Ramiel was a literal miss as well. However, in both cases, the second attempt succeeded (simultaneously, in this case). This one may be a bit more of a stretch, but it's all I can think of at the moment. The rest seem much more obvious now that I think about it:
Israfel: The whole ordeal is one big parallelism. It's the most flagrant one in the whole series.
Sandalphon: Ha ha! Thermal expansion.
Matariel: "Let's work together to accomplish our goal."
Sahaquiel: I don't remember this one very well. Someone else find the parallelism for me. It almost certainly has to do with Misato in this case.
Ireul: I'm not sure if this one really counts, since it wasn't actually an Eva battle.
Leliel: This fight is all about Shinji vs. himself. There's not necessarily a parallelism here since the human aspect and the angel aspect have become one.
Bardiel: Shinji certainly hit Toji back rather nicely... I have a feeling that wasn't the intended prominent parallelism, though, since that was so long ago.
Zeruel: Shinji finally starts to stand up for himself and make his own decisions right as Unit 01 obtains the S2 Engine. Greenfield or McCoy might have mentioned this one as well.
Arael: Same as with Leliel, but with Asuka instead of Shinji in this case.
Armisael: I'm guessing it has something to do with Rei's death and rebirth vs. Armisael's attempt to regenerate the dead Angels.
Tabris: Here, the parallels finally culminate in that Shinji's fight with the Angel is his interaction with a human. Even more than with Leliel and Arael, "the two have become one".
ITT we poke holes in my statements.
