Ibn Hazm Al-Andalusi writes that the only abrogated part of 2:178 is والأنثى بالأنثى
(and the female for a female). He does not give a reason for this statement. Here is what he wrote about this case in his book الناسخ والمنسوخ في القرآن,
الآية السابعة: قوله تعالى "كتب عليكم القصاص في القتلى الحر بالحر والعبد بالعبد والأنثى بالأنثى" 178 البقرة وها هنا موضع النسخ من الآية الأنثى وباقيها محكم، وناسخها قوله تعالى "وكتبنا عليهم فيها أن النفس بالنفس" الآية 45 المائدة. وقيل ناسخها قوله في سورة بني إسرائيل "ومن قتل مظلوما فقد جعلنا لوليه سلطانا فلا يسرف في القتل" 33 مدنية الإسراء 17، وقتل الحر بالعبد إسراف وكذلك قتل المسلم بالكافر
He also reports that some have said that the abrogating verse is
Clearly 17:33 does not abrogate anything because it forbids mindless retaliation and 2:178 reiterates that as it mandates a one-to-one retaliation which is also what 5:45 says. Dr. Mustafa Zayd points that out in his refutation of this claim in his book النسخ في القرآن الكريم, volume 2, pages 132-134 (item 872). He also offers a simple argument to refute this claim: Chapter 33 was revealed in Mecca, before Chapter 2 which was revealed in Medina!
Dr. Zayd also points out that the practice of the Prophet (PBUH) suggests no abrogation, since he had a freeman executed for killing a free woman. The consensus of the scholars, according to At-Tabari, in his exegesis, volume 3, pages 363-364, is that there has always been only one ruling about retaliation for murder.
The issue they were struggling with is whether a believer can be killed in retaliation for a disbeliever, a man for a woman, a freeman for a slave, etc. God doesn't say in 2:178 but He does in 5:45. The answer is yes; "a soul for a soul". In other words, 2:178 was specific for three cases only and 5:45 made clear the principle: "a soul for a soul".
This is the claim Abdul-Muta`aal Al-Jabri rejects in his book لا نسخ في القرآن...لماذا؟, page 122. His argument is that 2:178 speaks about retaliation, while 17:33 speaks about due process.
As for the claim that 2:178 was abrogated by 5:45, Al-Jabri praises Al-Layth's ruling that a male is not killed for a female but pays ransom instead. He sees that as a way to reduce bloodshed. I respectfully disagree; the choice of ransom is the murder victim's family's only, not the judge's.