256 color pngs will by and large almost always be smaller than 256 color gifs. Unless it's animated then your png will always be smaller since it doesn't do animation 8)

A rule of thumb: If you have a bitmap image, make it a PNG, you will save somewhere from 50-85% of the file size. If you have GIF, convert it to PNG (if it's not an animation) and you will usually save about -5-10% (yes virginia, there is a negative in front of that five) of the file size (in cases with very small images with very few colors, sometimes GIF comes out smaller, there's not many cases I've seen of that though xD).