For this fight, I will be using both at their argued peaks as relatively normal humans. For Logen, I will be using him as of the original First Law trilogy, specifically while during his fight with Fenris the Feared. Also, he will already be in the Bloody Nine state as of the fights start. For Clegane, this will be during his fight with Oberyn Martel, as this is his most powerful point in terms of physical power before getting all zombified.
For kit, I will be using them as of their last duels, with Logen having the makers longsword and a set of daggers, and the mountain having his greatsword and armor.
Logen Ninefingers was a barbarians of the North, and was a notorious and much feared warrior, know across the North for as the brutal champion of the chief Bethod. Due to a missing finger on his right hand, he is often referred to as Ninefingers or the Bloddy-Nine.
The Makers longsword: Being a magical blade created by Kanedias thousands of years ago, Logen's preferred sword was itself a magical and otherworldly blade. While noted for being an ugly and grey weapon, Logen's sword is incredibly powerful on the swing, being able to split an armored warrior in half from shoulder to waist with a single blow, along with cleaving off armored limbs and just about explode the skulls of Shanka. The weapon sword a longsword, being 2 handed and sporting a crossguard.
Daggers: "You can never having too many knives" was a philosophy Logen followed. During his time in the first law trilogy, Logen is almost always shown carrying at least 1 and upwards of 9 knives hidden on his person, even when out of combat. These knives were never fully described, but were likely of numerous different designs, from ones suited for thrusting to ones suited for cutting, all likely being around a foot long.
Ser Gregor Clegane is a is a knight of House Clegane, and was a notoriously fearsome and brutal, with a tendency toward extreme and excessive violence. Due to his huge size, he is called "The Mountain That Rides" or more often simply "The Mountain".
Greatsword: A hulking weapon of great length. Gregor's greatsword was massive, being meaty blade designed to smash and hack through an opponent. And accordingly, the sword was able to do incredible amounts of damage, with single swings being able to decapitate a horse with a single. The sword seemed to be roughly 5 feet long and sorted a 2 handed grip, though Gregor generally used the weapon with just one hand.
Plate armor: Gregor wore a suit of Westerosi plate armor. The armor was decently well constructed, being composed of a metal helm, a mail hauberk, a segmented cuirass and mantle, pauldrons and a skirt of hanging plates. This armor was decent in construction, being well suited to protect against slashes and cuts. However, the armor only lightly covered the lower body and seemed to have weak spots on the underarms, with Oberyn getting through both. Also, the cuirass was composed of two different pieces of steel and had a thin gap between them, which we saw Oberyn impale him through near the end of his fight with him.
Having spent most of his life fighting in some way, Logen was a highly seasoned warrior. He would spend a lot of his youth fighting either aggressive warrior bands of Shanka (pretty much big apelike orcs) and occasionally clashing with out barbarian peoples. After becoming Bethods champion, Logen would have a long and brutal careers as a soldier. He would fight in 3 stretched out campaigns, fight in 7 pitched battles, 11 honor duels against opposing chiefs or champions, and dozens upon dozens of skirmishes and raids. And in his time, Logen has fought against impossible odds, slaughtered dozens of men or Shanka in battle, and even defeated Fenris the Feared in a duel, despite the mans supernatural demonic tattoos and dressed in plate armor, even while the Feared strength was being magically enhanced by the sorceress Caurib.
The Mountain was a well seasoned warrior for his time, playing a major part in the Lannister war effort during the war of the 5 kings and played lesser parts in both Roberts Rebellion and Greyjoy's Rebellion. During Roberts Rebellion, due to his allegiance to the Lannisters, did little fighting up until the sacking of Kings landing. He would later fight as a part of the Lannister forces during Greyjoy's, though he wasn't noted for doing much in this conflict. Where he would really cut his teeth was his acts in the war of 5 kings, being ordered to pretty much attack and set the Riverland's ablaze, cutting and bloody swath of death and rape throughout the Riverlands. He would eventually fight a duel with Oberyn Martell, where he would be out fought but still win after taking advantage of a single unfortunate moment. Beyond battle, Clegane participated in several tournaments, being known for his "accidental" killing and maiming of his opponents.
While already incredibly impressive outside of the Bloody-nine transformation, Logen's physical capabilities and swordsmanship abilities sharply increase while fighting as the Bloody-Nine. Most notably, as the Bloody-Nine, Logen didn't feel pain, with the best example of this being his duel with Harding Grim, where the Bloody-Nine ran up the length of a Grim's spear shaft just to get into melee combat with him. His strength and agility where also pushed to the upmost human limit, with Logen effortlessly overpowering larger men like the baseline Fenris the feared and the Stone splitter, along with tearing off practical Halims head with a blunted sword. He could also move at incredible speed, being able do dodge multiple attacks from multiple Practical's, Northmen or Shanka in pitched fights.
Being a towering giant of a man, Gregor Clegane was noted for his incredibly levels of strength and hardiness. Standing at roughly 7 feet in height, the mountain experienced a solid reach advantage over most warriors. In pure terms of raw strength, Gregor was strong enough to crush skulls with his bare hands and lift a fully grown man of the ground with the point of his sword. He was also extremely resistant to damage, continuing the fight Oberyn Martell after sustaining several wounds, one of which was a spear through is mid section. But where the mountain deals with an issue is with his general lack of dexterity and agility. While he was strong, his sword swings were slow and comparatively clumsy, getting completely out maneuvered by Oberyn Martell.
This battle will take place in a trial by combat in a hypothetical fight between the Union and the Lannister's. Logen will already be in his Bloody-Nine phase. The battle will take in a amphitheater, looked over by both Tywin Lannister and Lord-Marshal West. The fight will be to the death.