The best way to begin is to listen to the difference between a stratocaster and a les paul by going to a music store and playing them back to back, but through the same amp. This will allow you to hear the difference between a stratocaster and a les paul, and judge for yourself which of the 2 sounds you like the best, and which sound matches up with the guitar music you like to play.
Other differences in sound between the Strat and Les Paul could be attributed to major design differences. For example, the Les Paul neck is a set neck, connected to the guitar body. While the Strat is a bolt on neck. Also, the Les Paul has a fixed bridge that doesn't move, and the Stratocaster has the moveable bridge with the whammy bar.Tone Difference
A lot has been said about thedifferences between the famous les paul and stratocaster. The main difference is in the pickups, with the Les Paul using the Humbucker and the Strat having the single coil pickups. Some could argue that a lot of the difference in tone could be made up for is amp settings and other electronics. It really comes down to you being the judge and trying out a lot of Pauls and Strats and judge for yourself which is best.