This difficulty will make driving more demanding and remove in-world navigation signs from the streets. Police will also be much more aggressive on Classic, with even driving a little over the speed limit causing them to come after you. Enemies are also far more aggressive and can deal more damage to you. They also dont show up on the games minimap. Reloading will also forfeit any bullets you have in your clip, meaning you will need to pay attention to how much ammo you have left. There will also be a trophy for completing the game on this difficulty.
Source: N4G PC Mafia: Definitive Edition's Classic Difficulty Aims To Recreate The Original Game's Experience