In the course Fiqh of Criminal Law, Dr. Bilal talked about rational empiricism. He talked about contents of the American Constitution as an example in faults of human reasoning. He mentioned the injustice, ignorance and racism by considering a black man 3/5 of a white man. I was wondering, how different this is from an Islamic point of view where a slave has 1/2 the value of a free man; Christian, Jew or Magian will also have a lesser value than a free Muslim man; a Muslim man will not be killed for a man of different religion, etc. (Criminal law, Fiqh 401).

A black man in the time of the writing of the American Constitution in perhaps majority of the states was a slave. So in general, if that was written by Muslims, there would not be "a black man" rather "a slave" and in a way it would have the same value/meaning.

Is there difference only in a fact that them trying to be "democratic" they are able to come up with such a law, while Muslims would have (in a way) the same law set by the Islamic law system? Or is there any other reason why their ruling is called injustice and same ruling in Islam is just?

Historically, undoubtedly there has been injustice to the black man. Through the ages, a black man was in status and value lesser than the lighter skin and other classes simply because he was black. And the concept of slavery for the black man was extended simply because of the skin color held.  It was the previous dogma, which sadly is still held by the ignorant, that the black was inferior to the White simply because of the skin. Some even believed that this was endowed by the Almighty himself.

Islam does not teach us to discriminate people based on their skin color. Assuming one as a different color does not require them, at any period, to fall under slavery or lesser status. Allah holds people accountable for injustice.

As for a slave having 1/2  value of a free man in Islam, Christian,Jew, Magian having lesser value than a free Muslim man, a Muslim man will not be killed for a man of a different religion - these are statements which require further investigation and clarity.

Everything requires an established Islamic proof and authentic references. When we say the slaves value is 1/2 the free individual, it requires daleel, a clear statement of the Prophet (ﷺ) or Quranic verse which says the slaves value is 1/2 of a free individual.

When we compare the concept of slavery which was practised throughout History and the Islamic concept of slavery, we find that Islam calls to respect of the slave. That is why, through the ages, people of lesser value in other economies attempted to run away and live amongst Islamic Economies. There are many Ahadith which aid my statement.

One of the most powerful verses in connection to the distribution of zakah calls for the freeing of slaves. (Qur’an 9:60) This is a rarity in history particularly at a time and era in which slavery was part of the most powerful societies.

As an example of its conduct, it is attributed to Zain-ul-Abideen, the great grandson of the Prophet (ﷺ) that one day a slave girl was pouring him water for wudhu. She accidentally bumped his head in the process. So she reminded him of the verses of the Almighty “…and those who control/suppress their anger” So he said “I have done so.” So, the girl continued in her reminder with the next portions of the same verse “…and those who pardon people”. Husain bin Ali (رضى الله عنهما) said “I have done so”. The girl then continued on with the next portion of the verse “…and Allah loves the Muhsineen (righteous doers)." So Zain-ul-Abideen said, “You are free”.  (the verse recited is Qur’an 3:134) [1]

As for the Christian, Jew, Magian etc, to say that Islam considers them of lesser value requires a proof from the Qur’an or Sunnah.

The statement that a Muslim man will not be killed for a man of a different religion needs to be checked. The opinion mentioned refers to an opinion of the Jurists to a specific matter. However, when we investigate the concept as a whole, in the light of the Quran and the Authentic Sunnah, we will find that if a Muslim chooses to cause corruption in an economy, and directly kills a person from the people of the book, they will be held accountable for their actions. And for a serial killer, Islam does teach capital punishment. (as Malik bin Anas (رضى الله عنهما) explained)

Reference:

[1] [Al-Bidaayah wa an-Nihaayah 9/125]