None of your items, ships, or outposts carry over. Your level and all the skills you've levelled transfer over. Your powers are where it gets interesting. You can only get so many powers in a single playthrough. However in new game + you keep your existing powers and can add more. Additionally you can upgrade the powers from your last playthrough. So you can can keep rush through the main story over and over until you're basically a space god.
So based on how far you already are, you might want to just finish and restart so you can explore with more powers. It's a matter of preference though.