What am I doing wrong in photographing my coins?

If you keep using a single light source your results won't improve.

White Balance is important. Use Tungsten is available.

Use a grey background for the coin. The background that you use influences the camera greatly.

Keep experimenting

 

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There is a good deal of helpful advice in this post. I am always interested in what software people are using, along with camera settings and setup.
I don't think either set of pictures posted in the OP is bad, while it seems the second set seems to show more detail. Is the objective the most accurate rendition or the most esthetically pleasing?
So, which set is the best representation of how they actually appear, in-hand?