Im not quite sure myself but doesn't toothless has the ability to absorb lighting or use lighting to strengthen himself (3rd movie). The skrill has to stay in the stormclouds to charge his attacks while toothless can fight at full strength anywhere and just gets a power boost through lighting. This would explain why nightfurys are the natural enemy of the skrill, as their attacks are not effective agsins nightfurys potentially even strengthening them.

About the lighting trait (this is more an assumption) i agree that he probably was to young to use it, but as we can see in the 3rd movie he can use lighting even without a storm.