The answer to why the chachamim made a ruling to say the Shema not later than midnight is of "to keep a person far from aveira". Then, items of korbonos are compared. Rashi explains that the reason the chachamim decreed "not later than midnight" by the korbonos is that maybe he'll miscalculate daylight and eat them when it's already day and be chayav korais.
The worst situation that's seems possible if one is late saying the Shema is that a person missed an opportunity to fulfill the positive mitzva of Shema, but even so, he would fulfill the positive mitzva of learning Torah. Why is the comparison of "l'harchik ha'adam min ha'aveira" to something so "heavy" as missing the time of eating korbonos and being "chayav korais"? What's the aveira here?
It seems that the RAMBAM may have also been bothered by your question. When he discusses the obligation to eat the meat from the Korbanos before midnight (Hilchos Ma'aseh ha'Korbanos 10:8), he says that it is "in order to distance a person from Aveirah ," which is the wording used by our Mishnah. But when he discusses the obligation to burn the Ketores before midnight (Hilchos Ma'aseh ha'Korbanos 4:2) and the obligation to recite Shema before midnight (Hilchos Keri'as Shema 1:9), he says, "... in order to distance a person from Peshi'ah !"
The Rambam replaces the word that our Gemara uses, "Aveirah," with a different word -- "Peshi'ah." The word "Peshi'ah" has less severe implications than the word "Aveirah," and it implies that the person transgressed a positive command (which is not as severe as transgressing a negative command, as you mentioned). Hence, the Rambam indeed learned that the comparison between eating the meat of Korbanos past its time and reciting Shema past its time was not an absolute comparison.
However, this begs the question. Why indeed does the Mishnah compare reciting Shema too late to eating Korbanos too late?
It must be that since it is extremely common for people to delay saying Shema and to fall asleep without having fulfilled the Mitzvah, the Rabanan used a severe comparison in order to ensure that people would not slip up. This is the implication of the Gemara later on 4b.