Classic question...classic answer is you can usually go one tire size without changing handling or encounter clearance problems. Any more and usually will have to do subtle mods of some kind, (some of which escalate other changes to compensate for side effects). Remember, HD has had many years of R&D to tune the suspension and handling balance of a mighty fine machine already.
Bottom line, if changing ONLY the tire, any improvements are usually cosmetic, bigger also means more unsprung weight, lead to less tire patch loading (while sometimes even result in a smaller tire patch due to sidewall pinching (to wide tire for wheel rim width) changing the profile and handling characteristics. All things being equal, if you only change the tire you could do better just by the difference between a semi-worn tire and new tire.