Thematically: The original Rallyman was based on Rally driving whereas Rallyman: GT is based on Grand Tourer races.
Mechanically: Rallyman and Rallyman: Dirt were solo play games where players competed for the best time and had very little impact on one another. Rallyman: GT uses the same core mechanics but has been tuned to be a head to head racing game with more player interaction.
Material: Asides from all the material being lovingly re illustrated, the biggest change is with the tracks themselves. In the original the tracks were printed on A4 boards and by connecting two pieces of track together you got a race course. However, aside from being a bit of a spaghetti mess, the number of tracks was still limited. Now the tracks are on hexagons which allows us to scale everything up and provide you with complete freedom to make any kind of track that you can imagine!