"Figure out" refers to a situation when someone is presented a problem or a puzzle. One might say, "I figured out the problem". A synonym would be "solve". "Come up with" can be used in a more general sense, meaning to produce an answer or suggestion. "I came up with a list of things to buy for the party".

Figure out is phrase we use when we want to solve a problem or find a solution. For example: 1. You'd figure out how to solve a problem. 2. You'd figure out how to get somewhere new. Com up with is to generate a new idea. For example: 1. Innovative companies come up with new products. 2. Friends might come up with plans for the weekend.

These are interchangeable and I can't really think of a context where one would sound right and not the other, both of them mean to solve a problem. "The events last weekend have brought this issue to our attention and we need to figure out a solution." "The events last weekend have brought this issue to our attention and we need to come up with a solution." Sorry for the boring example sentences :(