I have not played those modes yet, but I have spent about 8 hours in the campaign - I love it.
It's different from 2/3/4 (3 and 4 were prettumuch the exact same game). The exploring is far more organic - no more climbing towers to unlock areas and fill the map with icons. This is much more Skyrim-like in that you explore the map to find things, and, once you leave the first small island, the entire map is open to you. It's really fun to walk/drive around and explore. Thankfully, there's no more hunting to craft items. The progression / perk system now relies on doing things to earn perk points. There are a ton of "challenges" that once you meet them, you get the amount of perk points they are worth (for example, kill 10 people with a pistol - that's two perk points.. Kill 40 with an assault rifle - two more. Ten stealth kills - there's more. Kill three deer - there's another. And so on. Each challenge is one-time only, so you can't keep earning them over and over.) Basically, this encourages you to use all of the weapons, and at least experiment with different styles.
It looks like there are some cool sandbox things, like the arcade and user-made levels. I have not dived into that at all yet, but am looking forward to doing so. I also noticed a neat "reset outposts", which repopulates outposts if you want to re-take them. There are also real sidequests now, and some puzzle areas (prepper stashes) that are fun to do.
They basically kept all of the good that you expect from Far Cry (combat is fun / it's a little goofy, but not overly so), but changed enough that this feels really fresh (much better than the 3 to 4 jump, which was minimal). AI can still be a bit dumb, but that's Far Cry.
Bottom line: It's different enough from 3/4 to make it feel like a new game. I feel it's well worth $60, so if you were on the fence, I'd say go ahead and buy it.