Body
The Les Paul has a solid mahogany body with a carved top, while the Melody Maker has a solid mahogany body with a flat top. The Les Paul's carved top gives it a more pronounced "bump" at the bridge, while the Melody Maker's flat top is more streamlined and sleek.
Neck
The Les Paul has a set mahogany neck with a rosewood fretboard, while the Melody Maker has a bolt-on mahogany neck with a rosewood or laurel fretboard. The Les Paul's set neck provides a more sustained, resonant tone, while the Melody Maker's bolt-on neck offers a brighter, more articulate tone.
Pickups
The Les Paul has two humbucking pickups, while the Melody Maker has one or two single-coil pickups. Humbucking pickups are known for their warm, full sound, while single-coil pickups are known for their brighter, more articulate sound. The Les Paul's humbuckers are mounted in a "soapbar" style housing, while the Melody Maker's single-coils are mounted in a traditional "bobbin" style housing.
Hardware
The Les Paul has a Tune-o-matic bridge and stop tailpiece, while the Melody Maker has a wraparound bridge and tailpiece. The Tune-o-matic bridge is known for its stability and intonation, while the wraparound bridge is known for its simpler design and ability to provide more sustain.
Price
The Les Paul is typically more expensive than the Melody Maker. This is due to a number of factors, including the Les Paul's more premium materials and construction.
Conclusion
The Gibson Les Paul and Melody Maker are two great electric guitars that offer different players a unique playing experience. The Les Paul is a classic choice for rock, blues, and jazz guitarists, while the Melody Maker is a great choice for players looking for a more affordable, versatile guitar.