Do you mean, which son of Jacob are you biologically descended from?
Are you actually a physical descendent of Jacob? Not everyone is, of course, but if you are, it would be pretty neat to know which son you came from. But spiritually speaking, it makes no difference at all.
The New Testament doesn't really talk about this at all. A much bigger NT issue is Israelite v. non-Israelite, and on that issue, Ephesians 2 is pretty clear that both groups have been joined together, united in Christ.
By the way, where does the Bible say that God doesn't favor one tribe or another? It seems to me they all messed up pretty badly, and all 12 tribes were judged, in two groups, Judah, and Israel (everyone else, sometimes referred to as Ephraim because it was the largest tribe). Just read the prophets, it's all throughout those books.
But I think the key here is this: If you're trying to do God's will in God's power (not your own strength or self-righteousness) and trusting him alone, then God already favors you! The very fact that you want to do God's will and that you have spiritual fruit in your life shows that God has given you grace and saved you. Just remember, you can't do this yourself, you need God to be working in your life; but if you see God working in your life, then he won't stop! And make sure that you also don't stop following his will. (Phil. 1:6; 2:12-13)