Theokoles would best the egyptian and here is why:
They are NOT the same in immunity to pain. Theokoles let Crixus sword go right through him and felt nothing. The egpytian does feel pain but he is just a strong guy. He shows it when Oenomaus slashes him and punches the wound and even goes "oww" when Gannicus cuts his arm.
Pain resilience - Theokoles.
When Striking Theokoles is shown to shake shields with his strikes and flipped Spartacus into Crixus. Then after Spartacus trapped Theokoles' sword under his shield before using the handle of his sword to hit him in the mouth Theokoles smiles before flipping him up in the air. The Egpytian broke a guys neck with his bare hands. His punches and kicks are deadly both floored Crixus and Gannicus. Theokoles headbutt on Crixus knocked him off balance but in strength I think Theokoles takes this one.
In speed we see the egyptian responds well to attack and is able to move backwards and dodge Gannicus' strikes before retaliating. After being shot in the leg with an arrow reducing his speed capability the Egpytian manages to speed walk his way and kill Lucuis. Theokoles doesn't show anything of being able to be quick apart from charging into battle.
Speed- The Egyptian
Theokoles is shown to have devestating attack and in Oenomaus' words "A game of blood of amuse the crowd and when he tires he will move to seperate your head from your neck." That may not be totally word for word but it stands the same that he draws out the suffering of his opponents before killing them. Crixus recieved two huge wounds and was about to be killed by an older Theokoles. The Egyptian managed to kill rebels with his two daggers or his khopesh. He blinded and then killed the wounded Oenomaus who whilst not in his Prime defeated Agron in a duel (fight).
More Powerful Attack- Theokoles
Defense is crucial and The Egyptian is much more skilled in defense and counter attack then in straight up attack. Allowing both Gannicus and Oenomaus to throw the first strike so he can defend it and then strike in retaliation. Theokoles in his matches is often chooses to be careless since the wounds inflicted don't really bother him so the egyptian defintely takes it on defending against enemy combatants.
Defense- The Egyptian
Another important element is skill in facing more than one opponent than once. Theokoles in the show took on both Spartacus and Crixus whilst the Egyptian took on Gannicus and Oenomaus although not necessarily at the same because they took shots whilst the other fought nearby Romans. Theokoles only weakness was exposed by Crixus who used the reflection of sunlight and blinded Theokoles temporarily whihc was long enough for the losing Spartacus to gain advantage and kill him. When the egpytian fatally stabs Oenomaus Gannicus throws the Roman holding him back to the ground before kicking the egyptian of Oenomaus, kicking him to the ground, disarming him of his sword before shoving his sword into the egyptian's skull. Gannicus killed the Egyptian in 20 seconds. I feel that Close Quarters Combat of these two characters and is not demonstarted well enough but it is said that Theokoles once killed a 100 men in the Primus so I believe Theokoles gets this round,
Close Quarters Combat- Theokoles
Fighting skill without the sword is our final point of brief analysis. Theokoles was shown to be able to headbutt and punch and use very mild brawling skills amplified by his immense strength, Closer to actual martial skill is the egyptian. He plans carefully with his punches and even dropkicks Crixus to the face. He is more specialised in fighting so its fair enough that the egyptian wins this round.
Fighting Skill- The Egyptian
Theokoles Wins: Pain resilience, Strength, More powerful attack, Close Quarters Combat.
The Egyptian Wins: Speed, Defense, Fighting Skill.
Whilst The Egpytian has some indetifiable Strentght and Speed and would get a few shots at Theokoles he would shrug them off before playing his "game of blood" before eventually dispatching The Egyptian to the afterlife.