So you have a fancy image, all anti aliased, gradient effects and whatnot. You then decrease the colour depth and finally assign your palette of choice (presumably from the game or what will soon be in a game)?
Assigning a palette will tend to make things try to be fitted to it. This is not the most accurate process out there, depending upon the program it might even be very basic (most common, keep that, fit everything else to that).
Decreasing colour depth will do better for the colours as in many things it will account for more of the image when sorting colours and thus try to prevent issues with losing gradients/making their steps massive and what have you, it may also highlight some issues if something goes completely the wrong way and assumes one colour is closer to another.
Not knowing what program you are using here I can not say what its actual workflow is but I would not be surprised if the modern one does a better colour depth reduction as part of the chain.
All that said. Make sure you have backups and try it each way for a few different things and see the results.