It depends on the rest of your sentence. " I believe I will" expresses willingness, sometimes called volition. Sometimes it just expresses future time, but in current English " I will be going to" and simple present "I will" can also do this. "Would" is often called the past of will, but it also expresses other thoughts. It can mean willingness to perform a hypothetical action, such as, "I believe that I would help you, if you needed help." In this sentence, you do not need help, but I would help if you did. "Would" can also be used to express habit in the past, as in "When I was a child, I would sleep with my teddy bear."

Would is the past tense form of will. It is a modal auxiliary verb. After would, infinitives are used without to. I would like some advice. (NOT I would to like some advice.) She said that she would come. (NOT She said that she would to come.) Questions and negatives are made without do. Would you like to come with me? (NOT Do you would like to come with me?) He wouldn’t come. (NOT He don’t would come.) Note that the contracted form of would not is wouldn’t. Would and Will Would acts as the past tense form of will in reported speech. In other cases, would is a more polite form of will. Direct speech: She said, ‘I will come.’ Indirect speech: She said that she would come. Would is used in requests and offers. Note that would is more polite than will. Would you move a bit? (More polite than ‘Will you move a bit?’) Would you mind opening the window? (More polite than ‘Will you mind opening the window?) Would can be used to talk about past habits. The old man would sit in a corner and talk to himself for hours. She would always bring us nice little gifts. Would and used to Both would and used to can be used to talk about past habits or repeated actions. But note that only used to can refer to past states. He used to be a chain smoker. (NOT He would be a chain smoker.) The above sentence means that he is not a chain smoker at the moment, but he used to smoke a lot at some point in the past. Would is also common in sentences referring to unreal or uncertain situations. I would tell you if I knew her name. He would have helped you if you had asked him.