No meaningful difference. However, "to tend to do" is used in the active voice. "The children tend to make noise while playing." The others are more formal and are used in the passive voice ("to be inclined to do" and "to be prone to do"). "The children are inclined to make noise while playing." "The children are prone to make noise while playing."

Take note of what Chris has written. The idiotic down voter has struck again. I corrected the idiocy by voting Chris's comment back up.