I've only played SSZ, and I would say it about equal difficulty. I've beat both games without any significant hardship. This is a rogue game so the idea is that in the beginning you will die, but you get to keep your money and upgrade the ship so that each run "gets easier." You can also change the difficulty at any time (you get less money on easy though).

Not sure about joystick support, I play with an xbox controller.

Yes it has a story. There are in mission mini quests (like protect this ship, etc.) It is primarily combat focused however.

Ovearll Everspace is a really awesome, fun, and pretty game. The developers are really great and take user feedback. I've logged in over 100 hours thus far.