The way I look at the two is,
"figure out" implies you put more work or thought into something than just plain "figured" or "figure"... also that your conclusion or answer with "figured out" is more likely to be correct than just plain "figured" or "figure", it shows more of a thought process and confidence to me.
"I figure we should take the road heading east."
You made a decision to go east but the reason for going east is not 100% clear in your mind, a guess or hunch?.
"I figured out we should take the road heading east.""
Sound like you are more certain about your decision. Sounds like more thought was put into the decision so it is more likely to be correct.
Hope this helps a bit
- For Teachers