It's not just you, a bicycle will always have much more responsive handling. Mopeds have small wheels so they need a long rake and wide tires compared to a bike, to make the steering stable and the contact patch larger.

Higher rake means the bike pitches in response to the wheel turning, because the contact patch is less in line with the handlebars. Wide tires multiply that even more. That gives stability at high speed but when you try to turn the whole vehicle moves the wrong way, making steering lag. It also makes it harder to stay up.