1. The most apparent comparison is that in both stories, the main character dies. In some sense, both characters know they will die, as Seymour commits suicide, and Teddy speculates in his journal he may die that day.
2. In both, the characters are depicted as having some form of mystical knowledge. In "Bananafish," we have the symbolism of Seymour's name, while in "Teddy" the boy comments on having been a guru in a past life.
3. Both stories have the main characters speculate on the symbolism of the sea: Teddy comments on the appearances of orange peels floating in the water, and Seymour on the bananafish who get stuck.
4. Both stories have a rather grim theme of self-transcendence or enlightenment, although this is depicted through their deaths. Similarly, both stories show that the mundane world does not or can not understand transcendence.