With Open-World games, I often find myself asking what the "Open-World" is used for in telling the story and how successful a job it does at that. And some Open-World games use their "Open-Worldness" very well while others don't. The games that don't use their "open-worldness" very well is when I find myself asking why the game was "open-world" to begin with.
However, there are some general things all "Open-World" games seem to use the open world for. Combat and NPC interactions and backtracking are the big ones. All open-world games are used for those... or at least, they should be used for those. Backtracking in the "Open-World" is probably the first criteria that determines how good of an "open-world" a game has. Generally speaking, the more a player can backtrack, the better of an open-world the game has. It's the things other then those that really make or break "open-world" games for me. If a game just has those three, then I'd say that's when it becomes more iffy if a game should have been open-world or not.
I think it's really hard to talk about what an "open-world" game is without talking about The Elder Scrolls series of game (and probably Fallout, but I didn't play that series). The Elder Scrolls games have been doing "open-world" games for longer then most and it's very interesting to see exactly what the open world is used for and how it is used in that games series. On the one hand.... yes, the open world is used for Combat and NPC interactions and backtracking. It's also used for world-building and character interaction with the world. Simple stuff like opening containers, rearranging objects in the world, dropping items from your inventory and seeing them appear in the world, and things of that nature ground your character in the world. And those aren't things you can easily do without the open-world. Your character has an impact on the world in small ways that makes you feel like a character in that world.
And that is expanded to other things like questlines. Find out that shopkeeper is stealing from graves to get their stock and they'll go out of buisness and you'll never be able to buy from them. Join that guild and how you'll have access to their shops. In Morrowind, you could completely screw over the MSQ by killing characters you would have to turn quests into (killing off Vivec early turns this concept on it's head). The Elder Scrolls has many ways outside of the MSQ that let your character effect how parts of the world turn out (some of them on rather major scales to boot).
Of course, one of the trade-offs is that you can really easily kill the momentum of storytelling by dropping the MSQ and go doing something else. Decide to not go track down that king's bastard after you leave the sewers and never even start the MSQ? Sure. Go for it. Think anyone who thinks you are the Nevrarine doesn't know what they are talking about and want to ignore the whole thing? No biggie. The Elder Scrolls are just fine with people ignoring the actual main plot of the game even if it makes for a messy story-telling experience because their game designers know (or at least, knew at one point) that's one of the trade-offs for making a good Open-World game.
The problem starts when game devs want a tighter story-telling experience while keeping the feel of an open-world game. Out of necessity, this limits how "open" the world can actually be. Especially when it comes to backtracking. A lot of the point of an open-world game is going where you want to, when you want to. When stories call for areas to be inaccessible or a character not to leave a certain area, they directly go against this idea. Doing this is small bursts (like for a dungeon) is one thing. Doing it for entire sections of the game's story (like entire chapters) is very different.
When combined with side content that doesn't effect a world (FFXIII's side quests (or lack thereof) for example) it kinda begs why a game is "open-world" to begin with. Being able to go everywhere at almost any time in a game is rather pointless when nothing a player does impacts things in some way. And if the MSQ that a game is trying to tell railroad's a player so often, you kinda wonder if it would be easier for the story if the player wasn't allowed to go everywhere. I can't help but think that if "open-world" games are here to stay, then the storytellers of games need to realize that the old way of telling linear stories does not work for those. Looser stores do work though, as do stories that involve changing things in the game world in some way (even more if there's different decisions a player can make).
The strength of "open-world" games in my mind is that they allow for the player to be more connected with the world then are playing in then usual. However, it feels like most "open-world" games don't take advantage of that extra contentedness and simply use "open-world" games as extra set-dressing that looks pretty. And then realize that their story runs into problems when players want to go somewhere else then where the story says they should go.
Okay... I really didn't mean to type up this much on the topic...