The system in 3.5e sounds a lot better than 5e. You can perhaps justify the + Dex modifier in 5e with the argument that although bows and especially crossbows don't shoot with more energy if used by a trained person (bows could be drawn further with more strength, ok, that's the reason why Str should govern bows and Dex should govern swords ...) the trained user (symbolized by Dex) can hit vulnerable parts of the target better, so causing more damage. Using a whole action to load a heavy crossbow (which only has 5 damage compared to 4 of the light variant) seems a bit harsh, but loading with no cost is also bad. Crossbows were slow weapons, that should be modeled in some way.

At least we need the correction of the weapon sets effects, as The_Red_Queen said, I totally concur.