I find that, most of the time, I don't need to use the word 'problem'. So, I would say:
"We need to sort this out."
"Let's sort this out."
For me, 'sort out' refers to problems between people, like relationships or grudges, etc. Problems that involve both people. I use 'fix' for problems between me and the environment, like a broken computer or automobile. Also for problems between people that are my fault. For example:
"I lied to my mom. I need to fix this."
"My brother and I fought last night. We need to sort this out."
"I need to fix my broken computer."
"I need to sort out things between me and my girlfriend."
When I use 'sort out', I'm implying that both sides have problems. When I use 'fix', I'm implying that the problem is mine alone.
This is just my opinion, though.