I think the goal in FC3 is largely the same, but as I said earlier, I also lament the removal of some of those elements from FC2 that made the world feel more dangerous. On the plus side they did put a lot more emphasis on unanticipated behavior with animals, which works very well.
Either way, I think the "find your own fun" element is still very much there, and the game leaves things open enough for it. The objectives are largely similar to each other - typically "go kill this person/these people" - but there are different ways to approach and accomplish them.
You can probably just use a silenced sniper rifle to complete almost every objective, but if you want to mix things up, there are some fun things you can do. Leading a bear into an enemy encampment as a distraction while you start a fire isn't something you have to do, but it's certainly amusing. You don't have to stick a piece of C4 on an alarm, make yourself known to the baddies, and then blow it up when someone goes to trigger it, but it's a hoot.
The constant, intrusive in-your-face feedback with player rewards and goals is an annoyance, but it's also something I've become almost oblivious to just because it's been so common in AAA games for years now. I almost don't even notice it anymore, but I do wish it wasn't there. Achievement culture is what it is.