Why is Lord Rama considered to be a greater hero than Bharata and Lakshmana?
The most base answer to this would be that Lord Rama himself is the avatar of Lord Vishnu. Considered to be the source of all sustenance, Bharata and Lakshmana recognize this, as they are avatars of the Sudarshana Chakra and Shesha that serve Lord Vishnu. It is for this reason that Lord Rama is considered as the most superior figure in the epic. Aside from this, I think that it can be argued that both brothers follow the lead of Lord Rama when it comes to embodying dharma. Lakshmana displays moments in which his dharma wavers in his loyalty to Lord Rama. Bharata, through no fault of his own, is named as ruler when Lord Rama is placed into exile. I don't think that Lord Rama carries himself in a manner that shows superiority to his brothers. Instead, he offers himself as a mere vessel of dharma, humble and obedient to the will of the social order that guides his being. However, it is in this element as an example of how the path of righteousness should be followed by all human beings that Lord Rama emerges to be a greater figure than all else. Certainly, the devotion and love that both brothers show to him serve as testimony to this.