The three-digit codes are a shorthand, and #123 is the same as #112233. In the example you give, you’ve (effectively) swapped #FDFEFF for #FFFFFF, which is close to the original colour, but obviously not exact.
It doesn’t “matter” which version you use, as such, but three-digit colour codes mean you have a little less choice in shades. If you feel that saving 300 bytes is worth that, then go ahead and use the three-digit codes, but unless you’re designing for a low-bandwidth situation those 300 bytes won’t really save you all that much.