Well, the first sentence is incorrect. "We'll" (We will) is talking about the future, 'figured' is in past tense (verb 2). Im guessing you mean to say "we'll figure it out" (future simple).
In that case there is basically no difference in meaning between "we'll figure it out" and "we'll get it figured out".
The only thing that occurs to me as a native speaker is that I would tend to use "we'll figure it out" if it was a problem that me and the person I'm talking to are going to work together to solve. "We'll get it figured out" I would tend to use this if I was talking to someone who was less likely to be involved in the process.
This is a very, very, very tiny difference. I can't imagine a situation in which it would ever be correct to use one version and incorrect to use another one.