If we take a closer look at Yosef's work in Egypt from the day of his arrival until his demise, we can conclude that his actions were focused on the betterment of the nobles, the Pharoate and the country, with the underlying thesis that Bnei Yisroel were intended beneficiaries of Yosef's activity. Yosef realized that he was sent by God to settle and protect his family in Mitzrayim (as he told his brothers in Parshas Vayechi [50:20]), and he coordinated his efforts to this end by using his talents to lead the nation and gain prestige, so as to have the power to help his brethren. Thus, Yosef's charge to his brothers to tell Pharaoh that they were shepherds was a scheme to grant Bnei Yisroel land in Goshen, so that they could retain their identity and not assimilate into Egyptian culture. Similarly, Chazal explain that Yosef moved populations as part of his economic plan in order to protect his family. (See Rashi on 47:21.) Yosef sought to leave a lasting legacy in Egyptian society for the well-being of Bnei Yisroel, who would be treated kindly out of respect and appreciation to Yosef. It is for this reason that Yosef's engineering of the Egyptian economic plan is granted so much attention, as it was reflective not only of Yosef's hard work for the Egyptian crown, but it reflected Yosef's commitment to take care of his own people, and it is a lesson in Jewish leadership and mesiras nefesh.
On the other hand, Yehudah presents us with a totally different view. Although he rose to great prominence and eternal leadership (see 49:10), we know little about his life in Mitzrayim. The Torah only tells us (47:26) that Yaakov dispatched Yehudah to Goshen for instruction, which Chazal interpret to signify that Yehudah established a Torah learning center in Goshen. (See Rashi ibid.) Why is Yehudah's life in Egypt a mystery? He was already considered by the rest of the tribes to be a leader, so why is his role seemingly passive or silent?
The answer lies in the type of leadership personified by Yehudah. Rather than being a worldly leader, who internally cared for his people and strove passionately in the outside arena for their well-being, Yehudah portrays expressive and markedly Jewish leadership. He is typified by his conspicuous Torah identity, and his successors - the Jewish kings - were open Torah monarchs who were commanded to carry a Sefer Torah with them at all times. Thus, Yehudah's activities in Mitzrayim were not brought to full fruition, as they had to remain internal during that exile state, whereas Yosef filled the role of the external leader who interacted with the outside world.
It is noteworthy that Yosef, son of Rachel Imenu, was the leader in exile. He was indeed a spiritual offshoot of his mother. Just as Rachel did not merit burial in Hebron, the base of the Avos' residence in Eretz Yisroel, and she was intentionally interred at the roadside on the way to golus (exile) as a source of prayer and comfort to her children as they exited the land, Yosef similarly filled the role of caretaker of the Jews in exile. Rachel's mesorah is that of tending to Bnei Yisroel in golus, and Yosef thereby carried forth with this mission. On the other hand, Yehudah stemmed from Leah, who was the only wife of Yaakov to be buried in Hebron, the source of Jewish settlement in Eretz Yisroel. Leah embodies the mesorah of the Jew in geulah, at home, and her sons Yehudah and Levi thus filled positions of national leadership in terms of open Torah monarchy and Mikdash service.
May God grant His flock shepherds to protect them in exile, and may He soon restore the throne to Yehudah's progeny and His service to the hands of Levi.