First, in the Bible the recipient's father gave it. That is rarely true in Mormonism. Second, no lineage was given during the blessings in the Bible for they already knew what tribe they belonged to. The greatest difference, however, lies in the fact that the blessings given in the Bible all came true regardless of the actions of the recipient. In the Mormon Church, however, all prophetic blessings given are only said to be guaranteed if the recipient remains faithful to the LDS Church.
Any blessing given which fails to come true, then, is blamed on a lack of faithfulness.
This provides the 'insurance policy' for the myriad of blessings that have never come to pass. In such cases, the patriarch is let off the hook for prophecies that are obviously not given by revelation from God. Sometimes, these blessings even contradict other revelations given in the LDS Church. My own blessing provides one of these examples. My patriarchal blessing, given under the 'inspiration' of God, states very clearly that I am a direct descendant of Ephraim.