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I really like both of these games. They are both very similar to play (no surprise since STTDG was done after the author had played DSD6 and borrowed from the feel and mechanics liberally.
That said there are neat things about each system. DSD6 is a tighter, more elegant, more minimalistic game. You're really surviving a gauntlet. The threats come quickly and relentlessly. You are more likely to be overwhelmed. You only have 6 dice so the threat dice and infirmary are more of a problem. You're much more likely to run out of dice and lose that way. There is a commercial version of this game (though it's not really available yet). The art style is cool and it's easy to substitute in another player created ship (or another official ship).
STTDG is less relentless. The missions mean you feel like you have a purpose playing. The theme is stronger. The Developments mean you can build up your capabilities over time. You have more dice (which is important). There is a built in difficulty scale so you can make it harder or easier. With the Artscow components and custom dice it is a very pretty game but if you want to substitute in a new ship you need a new mat (more expensive).
I really like both games. I wonder if a second generation of DSD6 should import the mission idea or the development idea.