Well, in general, "I will" is future and unconditional, whereas "I would" is present and conditional. So you might say "I will go tomorrow" or "I would go, if you paid my train fare". The meaning just gets a bit complicated specifically when you are talking about yourself and your will, which you probably know now and can predict for the future. So "I will be willing to go tomorrow" becomes a bit redundant -- why wouldn't you just say say "I am willing to go tomorrow"? Or alternatively, if the thing it depends on is not certain to happen, you would use the conditional form. But if you are talking about someone else, "they will be willing to" do something is more plausible -- you know, but they don't, of some circumstance that will change their mind.

I have noted Elle's and James's good answers. Here are my observations purely from the practical point of "What do polite sophisticated native speakers say in real life?": 1. They say "I would be willing to (sit on the committee)" as an acceptance of an invitation without conditions, or even more likely to be the case "I would be happy to …" and "I would be delighted to …" In the U.K., "happy" and "delighted" are more frequently used than "willing" to indicate acceptance. 2. They would never say "I will be willing to …" except when negotiating. Example: "I will be willing to pay $X for the house if you leave all the furniture and the paintings behind." 3. In other circumstances, if they wish to say they are willing to do something, they simply say, "I am willing (to help you)", using the simple present tense. I think even in English language examinations, these are the accepted rules in the U.K..

In the technical sense "will be" indicates something that will take place in the future To say "I will be willing" indicates you are not willing yet, but that will change and then you "will be willing" To say "I would be willing" indicates (in the general sense) that you are willing right now. If you need a more technical answer (because "would be" also indicates future) please respond back. My answer is with the assumption that you are wanting to know the difference in context usage. "I would be willing" is the more commonly used phrase to indicate that you are agreeable to do something.

The difference is the same difference which always exists between "will" and "would". Here's a helpful link if you're not sure what that difference is: https://learnenglish.britishcouncil.org/en/english-grammar/verbs/modal-verbs/will-or-would