The concept of "Seven Deadly Sins" is not one exclusive to the Fullmetal Alchemist universe. It is also the core premise behind Nanatsu no Taizai, or Seven Deadly Sins, an anime following the adventures of Meliodas and his friends.
In both universes, the Sin of Greed stands out for his unique role in the story. For Fullmetal Alchemist, he is the only Sin to become a hero, and antithetically, Ban is arguably the most villainous of his group. This convenient dichotomy elicits an inevitable question; who would win in a fight?
10 Durability: Greed
It may come as little surprise that Greed's "Ultimate Shield" provides the perfect defense against his attackers. It is resistant against Fuhrer King Bradley's strikes (even snapping his blade in half upon impact), Edward's earth attacks, and virtually everything else in the series's universe.
Ban cannot boast similar feats, being regularly skewered, crushed, and obliterated by the many opponents he faces. The only way he could hope to manually circumvent Greed's shield is by attacking him before he could activate it — a feat Bradley exploited when defeating the rogue Sin.
9 Regeneration: Ban
As a human among gods and demons, Ban is significantly disadvantaged through the vulnerability of his mortal coil. However, his astounding regeneration reconciles for this weakness, as he is able to restore himself from being obliterated nearly into a pile of blood.
Unlike Greed, whose recovery is finite and fueled by his Philosopher's Stone, Ban's potential to regenerate himself is limitless. It is not a perfect defense; it sometimes takes him a moment to (literally) pull himself together, and should his soul be consumed, he would lose the battle. Given a homunculus's ability to consume souls (seen through Envy, Gluttony, and Pride), it would still not be impossible for Greed to put down Ban for good.
8 Skill: Greed
Through his own merits, Greed may not be as elegant a fighter as Ban and his nunchucks. However, he has been placed in the vessel of the talented Ling Yao, a man capable of thwarting Gluttony and Wrath through martial competence and grace alone.
This grants him a significant melee advantage over Ban, whose tactics revolve around his ability to shrug off significant harm. Should he cut him down swiftly enough, he would be able to wrap him in chains before he can regenerate, similar to what he did to Gluttony.
7 Strength: Ban
As admirable as Greed's Ultimate Shield might be, it belies an absence of physical brawn, something that Ban does not share. Through grappling with his opponent, he is able to feed off their strength, adding it to his own. It is extremely useful against daunting adversaries such as the Ten Commandments, whose power usually overshadows his own.
He has staggering brawn even without stealing the might of others. Ban is able to kill average demons with a single punch and wrestle with Meliodas, and the ensuing destruction is enough to bring down an entire prison fortress. This greatly overshadows anything Greed is capable of.
6 Gear: Greed
Another advantage of co-inhabiting Ling's body is the arsenal of tools that comes with it. Using the claws of his Ultimate Shield as a natural offense, he does not need to rely on keeping up with physical weapons like Ban does.
His gear advantages are through the means of smoke and flash grenades. With this cunning technology, he can deny Ban his senses, granting him imperative time to swing the nature of the battle in his favor. From blinding Ban, he could choose to mount his own ambush or launch a reckless offensive.
5 Allies: Ban
Alchemy may be a weapon more capable of meaningfully injuring the Sins than the kingdom's knights could have hoped, but none among the alchemists are able to produce feats that Ban's allies cannot match or surpass.
Escanor is able to conjure fire that would put Mustang's flames to shame, Meliodas is faster and more lethal than Edward Elric could ever hope to match, and Merlin's ethereal and mysterious physiology surpasses the aggregate of Amestris's knowledge. Should Ban's allies assist him in the fight against Greed and his forces, the homunculus's fate would be sealed quickly.
4 Intelligence: Greed
Ban does not fight as intelligently as Greed because he usually does not have to deal with the result of his carelessness. The combined prowess of Greed and Ling is observable through his fight against Fuhrer King Bradley, where he poised the bulk of his attacks against the man's eye patch, his presumed blind spot.
Additionally, they have more restraint than Ban, able to fight carefully despite the tragic death of Ling's faithful servant, Fu. This juxtaposes the Fox Sin's arrogance, who decided to attack Meliodas amidst a castle siege because a mysterious voice promised to restore Elaine.
3 Magic: Ban
Ban's ability to sap the strength of his foes gives him an advantage over anyone primarily relying on melee attacks. However, there is another skill in his arsenal that would bode lethal: Fox Hunt, magic able to confiscate anything from his opponent's clutches, including their hearts.
Against the likes of Envy, Sloth, and Lust, this would not be useful, as they could simply regenerate what was lost. However, since Greed shares a human host with Ling, he is dependent on his heart and vulnerable to Ban's harvesting.
2 Enemies: Greed
When measuring the worth of a character, it is prudent to compare them to the threat of their enemies. The Ten Commandments were powerful, marauding across the countryside and slaughtering all in their path.
However, Father is stronger than what they could have fathomed in their wildest dreams. Through careful planning and manipulations, he is able to harvest the souls of an entire country at once, rousing the strength to challenge even God himself. This starkly overshadows the feats of even Estarossa.
1 Conclusion: Ban
Greed's martial maneuvering and arsenal may be superior to Ban's, but attacking him would necessitate getting in close, where the Fox Sin is at his best. Moreover, Ling's flash grenades and smoke bombs are purposed more for escaping than attacking. This would give him an opportunity to recover himself if Ban inflicted serious wounds, though it would provide his opponent an equal chance to regenerate himself.
Ban's Fox Hunt would be able to pass through Greed's Ultimate Shield as it is not restrained by corporeal objects. Accordingly, it would deny Greed his greatest asset and secure the fight in Ban's favor.