
You don't have to use NES colours or anything like that, just for the sake of learning it's often beneficial to cut down your colour count (16 colours would be loads for a sprite like this).
I've done a quick image to show the issues of yours and highlight where Helm was going with his edit. Helms is marked "a", yours "b".
-contrast in your image is lacking, Helm added more shading and highlight in his
-your sprite doesn't read easily: is that his arm off to the side or just more armour? How is he connected to his sword? This is more clear in Helm's edit.
-The helmet is oddly shaded and the horn has too much noise, it looks segmented and jagged.. Also, what was going on with your mouth?
That said, I like your sword more than Helms even though it uses way too many colours, the white edge is a nice contrast.
The upsized and despeckled images (very roughly) simulate how the eye will read the sprite, notice how helms use of contiguous areas of the same colour describes the form better, while yours has a lot of detail that amounts to noise in the design.
I hope this helps, what I think you need to do is focus on getting the form described more fluidly before you go crazy on the colour count: in normal art the number of colours you use doesn't really matter, but in pixel art if you use too many your art won't read like you want it to.
That said, welcome to the forums

hopefully you're the kind of person that can take criticism on board and learn, because it looks like you're coming from a pretty strong foundation.