Every car is slightly different in comparison to every other car, but unlocking the upgrades will further differentiate the cars from each other.
It's true that some of the cars have similar stats, a lot of cars have similar levels of acceleration or top speeds in their default state. Unlocking the upgrades from the races will provide bonuses and choices - for example you're not going to use both long and short gears or lightweight chassis and reinforced chassis at the same time since these options are mutually exclusive to each other.
The cars gained from completing Most Wanted races are already improved from their base stats and generally more prestigious cars anyway so these are an improvement over most, if not all, of the other cars in their base state - but a lot of this is down to handling and if you can drive one particular car well you'll generally always do better than driving a faster car or a lighter car.