A symbolic poem, by which I imagine you mean a poem that uses symbolism, is exactly that, a poem that makes use of various symbols to represent various ideas or feelings. An allegory, on the other hand, whether a poem, a story, or a novel, is a complete story, told on two levels, one being the literal level, the story that is being told, and the other being the level in which the entire story acts as a symbol of the point being made. Orwell's Animal Farm is a good example of an allegory, being a story about the animals and also representing Stalinist Russia. C.S. Lewis' Chronicles of Narnia is a series of allegories representing Christian ideas, stories that operate very well as stories, too.