Well, if you are just focusing on the element of manliness, then you would have to pick Okonkwo without a doubt. Obierika is a character who is notable to for his intelligence and wisdom and his friendship of Okonkwo even when Okonkwo has been exiled by the rest of the tribe. You might want to think of the way that Obierika questions the reasons that resulted in Okonkwo being exiled and how he supports Okonkwo through this entire time, helping practically and emotionally. It is also Obierika who gives a final tribute to Okonkwo when he leads the tribe in a ceremony of cleanliness.
If you think about Okonkwo in comparison, he is so desperate to be seen as a man that he deliberately places himself in situations that constantly show his manliness. Consider how Okonkwo deliberately involves himself in the murder of Ikemefuna, even though he didn't have to. He not only accompanies the boy, but then is involved in his murder directly:
He heard Ikemefuna cry, "My father, they have killed me!" as he ran towards him. Dazed with fear, Okonkwo drew his matchet and cut him down. He was afraid of being thought weak.
It is in Chapter Three that we begin to understand something of Okonkwo's upbringing and in particular his relationship with his father that has produced such a character as Okonkwo:
With a father like Unoka, Okonkwo did not have the start in life which many young men had. He neither inherited a barn nor a title, not even a young wife. But in spite of these disadvantages, he had begun even in his father's lifetime to lay the foundations of a prosperous future. It was slow and painful.But he threw himself into it like one possessed. And indeed he was possessed by the fear of his father's contemptible life and shameful death.
Thus we can see that Okonkwo's desperate desire to show himself as many--killing Ikemefuna, wrestling and so on--stems from how his father was not manly and a terrible fear that he might have inherited something of those characteristics. Thus, clearly the tribe would vote for Okonkwo in the situation you have outlined.
This is a great question. I believe that members of the Igbo tribe would vote for Obierika to represent manliness in their culture. While Okonkwo might vote for himself as the ultimate example of a man, the rest of the tribe would probably see Obierika as more fit for this representation because of his wisdom.
Obierika is an elder of the clan, someone who commands the respect of the other members of the tribe, including Okonkwo. Men come to him for advice and help in handling specific situations. Obierika is also the person who serves as a mediator between the Gods and their punishments. For instance, when Okonkwo is exiled for accidentally killing Ezeudu's son at Ezeudu's funeral, Obierika is charged with leading the cleansing of Okonkwo's compound. While doing this, he says that no one hates Okonkwo, they are merely carrying out the sentence of the Gods. The other men trust him, including Okonkwo, so this requirement is carried out somberly, but with no anger. Therefore, Obierika's actions are most effective in appeasing the Gods.
Okonkwo's manliness comes from his desire to NOT be seen as womanly. His manliness comes from fear of looking like his father. He doesn't come by it naturally and cannot think through problems, but focuses on the violence that he sees necessary to solve them.