Gameplay wise, the campaign is much simpler than in development in the following ways:
Kerrigan used to have several options available to her known as focusses, which determines just her abilities. At one point one could switch focuses in game. This has been reduced to her being able to choose from various abilities from 3 pillars with focus having no role.
Unit upgrades were originally much closer to wings of liberty and required the completion of various bonus objectives to acquire. When a set number of upgrades had been purchased, one could unlock an evolution mission. This was changed to one upgrade per unit because it was too similar to Wings of Liberty.
Destruction of worlds, a mechanic where the player could choose from various worlds for the swarm to consume to upgrade your entire army has been removed entirely, moved instead to Kerrigan and cut scenes.
Mission wise, there is evidence that entire storylines have been removed, including one where Kerrigan tricks Abathur into making his own replacement, who thin kills him. Given that Abathur is the game's Ensemble Darkhorse, perhaps he grew on the developers as well.