One similarity is that both Teiresias in The Odyssey and the Blind Seer in O Brother, Where Art Thou? tell Odysseus and Everett, respectively, that he is about to undertake a voyage that will be filled with many hardships. Teiresias says that, "After much suffering you may get home if you can restrain yourself and your companions," while the Blind Seer says that Everett "must travel a long, difficult road."
Another similarity is that both, in a sense, speak of salvation. The Blind Seer does so more directly, saying that Everett will follow the road, "even unto [his] salvation." Teirsesias's talk of salvation is less direct and less obvious. He advises Odysseus that after arriving home and slaying all the suitors, he should then carry an oar to a land where the people have never heard of the sea, salt, or ships and make a sacrifice to Neptune, the god of the sea, there, who is still angry with Odysseus for blinding his son, the Cyclopse. He then advises him to return home and sacrifice to all of the gods. Teirsesias assures Odysseus that if he does those things, especially making the sacrifice to angry Neptune, his life will be taken by the sea, but not until he is very old, full of "peace of mind and your people shall bless you." Telling Odysseus that he will die old, at peace, and with his people happy, is a way of speaking of Odysseus's prosperity, or salvation.
But there are also very many differences. For one thing Teiresias's speech is much more detailed. He advises Odysseus that Neptune will make his voyage home accross sea a very difficult one because Odysseus blinded Neptune's son. Teiresias also gives him many different pieces of advise to make his journey successful, such as don't hurt the sheep on Thrinacian Island and that he will find his home being ravaged by suitors that he must take revenge on.
In contrast, the only detail that the Blind Seer gives Everett is that he will see many wonderful things, including a "cow on the roof of a cotton house."