I have recently begun running games in what I would consider to be a truer sandbox than I have ever run before, and have been loving it. Here is what I do to keep it successful.
1) Make sure there are enough things the players know about and want to do something about.
When we started I simply gave each character two rumors, Keep on the Borderlands style about places, peoples, events, treasure, legends etc. Some were true, some where not. Even now, 8 months later, they are realizing some of their initial rumors were true and some were not.
If you do this, you should prevent one of the major issues you can have in a sandbox which is too many choices, not enough information. When you tell someone they can do whatever they want, unless they are a veteran, or someone who is already comfortable authoring their own story, they will simply be stuck. Why would you want to do X over Y? What could happen if we do X and not Y. By giving rumors they have heard something about X already, and have a goal.
If you do this well:
The players will be actively engaged with the world and want to learn more, and take actions in character to understand more. It is one of the most fulfilling feelings having the players be actively engaged.
If you do this poorly:
The players will be confused and not connect with things. They will be stuck not understanding why they want to do anything.
2) You don't need to tell the players what's going on in the world, but you need to know.
I did a lot of prep work for this campaign (Ok, I mostly did some work near where they started and slowly expanded it out as they explored more). Mostly I made a 10x10 hex map, 12 mile hexes (1 day of travel on roads gets them through 2 hexes at best). For each hex I had some location they could find (Alright, I only have 70 of them done, but they haven't gone near the other 30 hexes yet, I'll deal with that when they get there[Also, full disclosure about 50% of hexes are me taking something from another module and sticking it in there, their two main villages are Red Larch and Phandalin renamed.]), and made an encounter table for each hex type (I did finally finish this one last week, now I'm done, as long as my future adventures only use Forest, Desert, Savanah, Mountain and Swamp, I'm golden). I also made all the power groups in the region, decided what they want and gave them clocks (A concept I barely understand, but have bastardized to use in my game). In this way, as the players adventure and follow up on things they want, the various groups in the region advance their plans. When the player interact with someone from these groups I know what they want.
In this way I do little prep between games, but am still able to maintain the living world around them. The players can then choose what parts of it to interact with, and if they decide to go deep on one thing, I know what they should find.
If you do this well:
The world will feel like something living and breathing. Both you and the players will feel like the world could exist, that actions have consequences, and there is more to find. Travel should feel like an adventure, and the world should feel large.
If you do this poorly:
It will feel disjointed and like there are many deus-ex machinas. Events will seem random, and suspension of disbelief will be gone.
3) Tell your players up front that they can find things that will 100% kill them without thought.
I told them this up front, they have to this point fled from 7 or 8 encounters. They have even fled from encounters that I knew were easier than they could handle because they didn't have any information on these foes.
So for me, the biggest con is: You as the DM need to do a lot of prep beforehand. You should know the world, the people, and the places beforehand. Then you need to figure out how to start the players exploring all this you made. If you don't do it correctly it can feel chaotic, directionless, and like a slog. If you do it well both you and the players should be excited and surprised each and every session.
To give an example from my game yesterday. First, we hadn't met in a month, which is the longest break to date. So I had the players write some short fiction to explore their characters and their motivations. Everyone was on board. People were giving me new plot hooks, describing how they felt about events in the campaign history, making poems filling out backstory, it was a blast. Then, secondly, they set out to deal with one of the many problems they have. First 4 hour segment when they get out of town, random roll, orc bat rider attack.
Now why on earth would orcs be attacking the party so close to their home in broad daylight? The players wanted to know. Well, I already had the answer. Without going in to extensive detail, the party has made waves in many places (Those clocks I mentioned earlier have been ticking) and one of those groups, who happens to be able to order Red Fang of Shagras orcs around wants to press-gang the party to work for them.
So now, after a random encounter roll they have learned more about the world (They managed to capture one orc and get a few details from him). They are now worried about a new threat, and have another hook to follow up on. Completely of their own volition they bought land and are trying to start a business, so now they feel their business is threatened, and I don't actually need to do any more work for this plot line. If they choose to go investigate immediately, the situation will not have changed much, but if they wait, the clocks will tick and I will know what sorts of things could happen to them.
I have lots of words and thoughts about this, and might make a resource for others. But I can say without doubt, if you are willing to put in the initial work, the results are so amazingly worth it.