Short Answer:
The privileged Ibarra favors peaceful means, while Elias, who has suffered injustice at the hands of the authorities, believes violence is the only option.
Long Anwer:
Ibarra is a politically important character because Rizal uses him to voice ideas regarding colonialism and the nature of power in the Philippines.
Elias represents the common Filipino who is not only aware of the injustices done to their countrymen but would also like to deliver them from their oppressors. He is said to be the personification of Andres Bonifacio.