Drupada in my opinion did not value Friendship as Karna did.
Drona took revenge on him only for his mistake of not valuing the childhood friendship of Drona. Drupada did not help Drona during his poverty stricken period. Leave alone, help – he insulted him saying that a Kshatriya will not have friendship with a Brahmin.
Drona takes revenge on Drupada with the help of Arjuna. Drupada could not tolerate the humiliation. He wanted to take vengeance on Drona. In friendship at a time one should forget things, if the wrong in done by us. Drupada did not do this. He was bent upon defeating Drona.
On the other hand Drona did not view the situation like Drupada. Drona valued friendship, he helped Drupada even after slaying him. He returned him half of his kingdom. He pardoned him. He accepted his son as his student and taught him advanced military arts,though he was the prophesied killer of Drona. He helped Drupada for designing an apparatus to test the archery skill of Arjuna at the time of Draupadi’s Swayamvar.
Drupada worked hard for taking revenge on Drona.He wanted a son to kill Drona and a daughter to marry Arjuna. He respected Arjuna, admired his ability in archery, inspite of facing the defeat through him. He does a great putrakami yagna for this purpose.He takes the help of Maharishi Yarchar and Maharisihi Upayachar.
Dhrishtadyumna and Draupadi emerged from the fire.
Another unusual birth of a character in Mahabharatha emerging from fire and not from the union of a male and female.
Draupadi’s other names:
Agnijyotsna (light from Fire)
Krishnaa (meaning one of darker complexion)
Panchali (meaning one from the kingdom of Panchala)
Yajnaseni (meaning one born from a Yajna or fire-sacrifice)
Mahabhaartii (great wife of the five descendants of Bharata)
Sairandhri (an expert maid, her assumed name during her second exile in which she worked as Virat kingdom’s queen Sudeshna’s hair-stylist).