"Conflict" is an interesting choice of words—I assume you are referring to the difficulties with which the poet is struggling as he composes this sonnet. Shakespeare is here deliberately utilizing the tropes of romantic poetry and courtly sonnets—such as comparing the lover's cheeks to "roses" and her skin to "snow"—in order to criticize and subvert them. His difficulty, which is now clearly revealed to him, is that none of these tropes apply to his beloved, who is "dun" of skin and whose eyes are "nothing like the sun." On the contrary, the speaker is extremely aware that his mistress "treads on the ground" and that "false compare" would only serve to belittle his love for her. He knows that she is not conventionally attractive, does not hear "music" in her voice or think her breath sweet, so he finds it difficult to write a traditional love poem to her, but at the same time, his love for her is "rare" despite the fact that she does not fit into any of these conventions.
There may also be an element of self-mockery in this poem—if you look at Shakespeare's sonnets 1–126, written to a very traditionally attractive young man who fits the conventions of romantic poetry, he often compares that beloved to roses, nature, and the sun. It is simply that, in writing about his other love, the dark lady, he recognizes the inadequacy of these tropes in this context.