It's a huge difference despite the fact that my evolved pokemon has a higher CP!.
As you can see the bar above your Pokemon is more or less full depending on the evolution. This is basically because the more evolved Pokemon has a higher potential for its upper-limit on Combat Power.
So the reason it costs less after you evolved it is because you are further from filling that bar completely. As you get closer to the upper-limit on Combat Power, the Stardust and candy costs go up.
This upper-limit is also determined based on your current level, and the upper-limit will be higher after you have leveled.
The stardust cost is proportional to how much Combat Power it has compared to it's maximum. As Kevin Tian says below, this seems to ignore evolution. I initially believed that a higher evolution would cost at least some more. I was wrong.
The stardust cost as you approach the maximum is different sometimes (like the final power up on Vaporeon to reach 1,000CP vs the final one on Pidgey to reach 150CP), but it seems to be related to type, trainer level, or just how high the maximum CP is for the individual pokemon. Not the evolution.
Each species has a different maximum CP - 160CP is high for a Pidgey, but quite low for a Pidgeotto! Some species are naturally stronger than others, and an evolved form of a Pokémon will become much stronger than its previous form.
The higher the Pokémon's current CP is compared to its maximum CP, the more stardust it costs to upgrade.
If you evolve that Pidgey, you'll have a Pidgeotto at about 300-400CP, as it adjusts to the new species.