In theory, heat levels will change instantly. In practice not so much due to the flat cooktop surface carrying residual heat carried over from the pot and pan when lowering the temperature. From my experience, cookware responds much quicker to the changes made on gas tops vs induction tops.
It may be just the variance in models. I find that my induction range is very responsive. I can take a pot of water from a full rolling boil to a gentle simmer in seconds (like 1 to 3) and back to a full boil again in seconds. I was showing it to a friend that's used a gas range for years and his response was "Wow!"