Restatement of the Question: Why was Abel's sacrifice considered 'greater', 'more', or 'above' Cain's? Was it because they were different types of sacrifice, or was there something else at work?
Historically, there is a great amount of speculation regarding this passage, but this answer is constrained to Scripture only :
Answer 1: Because Cain was unjustified to doubt God. Following his offering, Cain allowed his hope in God to falter--where Abel trusted. It was not the type of offering that was offered that affected God; but rather, God was affected by the state of Cain's heart--after Cain had made his offering :
Cain's loss of "confidence/hope"--after the offering--was not justified. And, Scripture shows that God pointed this out to Cain :
Genesis 4:6, NASB: Then the Lord said to Cain, “Why are you angry? And why has your countenance fallen?
Even so, God still remained faithful, and proceeded to teach and advocate for Cain, forewarning Cain about the imminent threat of evil, and the necessity to overcome it :
Genesis 4:7, NASB: If you do well, will not your countenance be lifted up? And if you do not do well, sin is crouching at the door; and its desire is for you, but you must master it.”
The Nature of the Sacrifice was, and is, Irrelevant to God:
There simply are no bases in the text to justify an interpretation that God favors one type of sacrifice more than another--except God does favor sacrifices of the "heart" more-so than any physical sacrifice :
Scripture explicitly contradicts the idea that God favors any form of earthly sacrifice:
NASB Psalms 50: 7-8, & 14: Hear, O My people, and I will speak; O Israel, I will testify against you; I am God, your God. I do not reprove you for your sacrifices, And your burnt offerings are continually before Me. ... Offer to God a sacrifice of thanksgiving And pay your vows to the Most High;
Proverbs 21:3, NASB: To do righteousness and justice Is desired by the Lord more than sacrifice.
With Cain's state of mind/heart, he could not possibly be thanking God, offering to God a sacrifice of praise/thanks--which is what God desired; because, "giving thanks" implies acknowledgment and trust that what was given is good, but Cain doubted, having fear, and losing hope :
NASB Gen. 4:5-7: but for Cain and for his offering He had no regard, [lit. God did not see or look upon]. So Cain became very angry and his countenance fell. 6 Then the Lord said to Cain, “Why are you angry? And why has your countenance fallen? 7 If you do well, will not your countenance be lifted up? And if you do not do well, sin is crouching at the door; and its desire is for you, but you must master it.”
Cain's Sacrifice May have actually been Greater:
... if not for his state of heart afterwards.
Cain was wrong to lose hope, and perhaps should have taken comfort in the fact that God did not "look upon him, or his sacrifice"--sometimes, this can actually be a good thing :
This is what Cain did not understand. And, because of this, he erred in losing hope, becoming disheartened, when he could have rather been confident in the mercy and sovereignty of God.
The English Translation of "וַיִּ֣שַׁע" as "more good", "favorable, kindly, mercifully, etc," is not necessarily correct, but rather it may be more correct to interpret the phrase literally as "to look upon", i.e., as "God looked upon Abel's sacrifice, but not Cain's."
In fact, there is Scriptural Basis to believe it is good when God looks away :
Job 7:17-21, NASB: What is man that You magnify him, And that You are concerned about him, That You examine him every morning And try him every moment? Will You never turn Your gaze away from me, Nor let me alone until I swallow my spittle? Have I sinned? What have I done to You, O watcher of men? Why have You set me as Your target, So that I am a burden to myself? Why then do You not pardon my transgression And take away my iniquity? For now I will lie down in the dust; And You will seek me, but I will not be.
Job 14:4-6, NASB: You also open Your eyes on him And bring him into judgment with Yourself. Who can make the clean out of the unclean? No one! Since his days are determined, The number of his months is with You; And his limits You have set so that he cannot pass. Turn Your gaze from him that he may rest, Until he fulfills his day like a hired man.
Answer 2: Because God is Sovereign - NASB Ex. 33:19: And He said, “I Myself will make all My goodness pass before you, and will proclaim the name of the Lord before you; and I will be gracious to whom I will be gracious, and will show compassion on whom I will show compassion.”
This second answer is not satisfactory, because it is not "internally consistent" with the rest of Scripture, and doesn't offer much insight. This explanation paints God as an arbitrary dispenser of Justice--but if nothing else, God is always portrayed as acting in wisdom, mercy, and truth--never arbitrary in judgment.