Avram stood up to Nimrod (which meant him being sent into a fire). This demonstrated his ultimate self-sacrifice for God, publicly. What more did the Akeida accomplish?
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The Lubavitcher Rebbe (Likkutei Sichos Volume 20, Vayera #3) said that the difference between the two tests was that in the first test, Avraham did what any normal "holy" person would do. He lived his whole life to spread G-dliness, and here is the ultimate way to show how much you believe in G-d - That you are willing to give up your life for it.
The Akeida, on the other hand, had no "side" purpose. No one saw it, and moreover, it would have resulted in there not being a continuation of Avraham's mission in the next generation. Yitzchak's death would result in the death of monotheism. Moreover, Avraham didn't "have to" bring up Yitzchak, Hashem only requested it, Avraham had a promise that Yitzchak would be his offspring, etc. He had lots of answers.
Yet, he chose to do what Hashem told him specifically because Hashem told him to do so. This level wasn't there in the previous tests.
The fiery furnace was sacrificing himself, which does not go against Avraham's nature of being kind to others. The Akeida is sacrificing someone else, his own son no less (nature of father is to have mercy on his son), which was a direct challenge to his attribute of kindness, in which he excelled.
It is in this vein that it can be understood the gemara in Sanhedrin which says that the Avos were tested and David Hamelech was not tested - did King David have an easy life free of challenges? The meaning of the gemara is that the Avos underwent tests that went diametrically against their natures.
Based on your name, it seems that you are Muslim. Placing both these stories on equal veracity / historicity in Islam, but not necessarily in Judaism. It depends who you ask.
Avraham's binding of Yitzchak is in the Biblical text itself. The facing off with Nimrod and being cast into the fiery furnace is midrash.
And the details within that midrash parallel the details described in the Biblical book of Daniel (perek 3), where the protagonists are Chanania, Mishael, and Azarya, who are cast into a fiery furnace rather than bow to an idol. This midrash is perhaps retrojecting the story of the descendants onto the ancestor, the first monotheist, and is an example of a midrash which was not intended literally, making some theological point.
Though the idea that he would be willing to commit himself to the fire in such manner might well be pulled from his behavior in the Binding of Yitzchak where he was willing to give up his son, his very soul ('yechidcha'), whom he indeed loved ('asher ahavta'). To turn around and ask why the Biblical narrative is required after we have the midrash would be to have things backwards.
But besides this, if we are to grant the premises of the question, then there are all sorts of possible answers. I would say: from a psychological perspective, and despite the opposite by Iyov, people are often willing to be a martyr themselves but not put up those they love.