If the predicate is expressed by a noun, the verb 是 is placed after 究竟 and 毕竟.
If the predicate is expressed by an adjective, 是 is not placed after 究竟 and 毕竟.
毕竟 is often used with the words 虽然 , 无论 and 不论 .
Examples
他不论是什么样的爸爸,他毕竟是你爸
Whoever he may be, he is still your father
tā búlùn shì shénmeyàng de bàba, tā bìjìng shì nǐ bà
他们无论多么有钱,毕竟都是人
No matter how rich they are, they are still human
tāmen wúlùn duōme yǒuqián, bìjìng dōu shì rén
究竟 is also used in interrogative sentences to get an answer from someone.