Both the Boss OD-1 and OD-3 have a very clear and distictive sound. The OD-1 is based on the sound of Marshall JMP amp from around the mid to late 70s. Its sound can be heard on countless classic rock albums of that time. When you try the pedal for the first time you will hear it straight away regardsless of settings pedal and the amp you will play through.
The OD-3 is based on the sound of Marshall JCM 900. These amps were being made during the 1990s. The big difference between the OD-3 and OD-1 is: OD-3 does have more bass, more clarity, more treble, more volume and gain.
Both OD-1 and OD-3 do have a slight hint of mid-range. Maybe a characteristic of Marshall amps?