1. Both jiū jìng (究竟) and dào dǐ (到底) are adverbs which could be employed in interrogative sentences to express further inquiry, and they also have the function of strengthening the tone of the question. They usually precede the verb or the adjective in the sentence, if there is an interrogative pronoun in the sentence, jiū jìng (究竟) and dào dǐ (到底) should be placed before the interrogative pronoun. Jiū jìng (究竟) is more formal than dào dǐ (到底), they both could be translated as “on earth” in this case.
nǐ dào dǐ /jiū jìng zěn me le?
What on earth is up with you?
zhè bù diàn yǐng dào dǐ /jiū jìng hǎo bú hǎo?
Is this a good movie on earth?
dào dǐ /jiū jìng nǎ yí jiàn yī fú shì nǐ xǐ huān de?
Which dress on earth do you like ?
Jiū jìng (究竟) and dào dǐ (到底) can’t be used in questions end with ma (嗎) to stress the tone.
nǐ dào dǐ /jiū jìng qù xué xiào ma?
Are you going to school?
2. Dào dǐ (到底) can indicate a result has finally been reached after a long time or process, but jiū jìng (究竟) doesn’t have this kind of usage.
tā dào dǐ hái shì fàng qì le zhè gè gōng zuò jī huì.
He finally gave up this job opportunity.