The benefits of having multiple campaign arcs in a long-running or multitier campaign are many. First and foremost, it's like having slightly overlapping safety nets; no matter what the players do, their choices have a pretty good chance of landing them smack-dab in the middle of one of your campaign arcs eventually. The arcs are so encompassing and pervasive as to be nigh unavoidable, and if your players are clearly turned off by one arc, they have two others to choose from. Having multiple arcs gives players opportunities to decide which threat they care about the most, and I promise you, each player will have his or her own opinion on the matter, based on which arc ties in most closely with that player's character. Having three arcs also makes your campaign feel less like a "one-trick pony." Finally, there's the benefit of allowing you, the campaign's primary storyteller, to entangle plot threads and create opportunities or occasions when two or more arcs intersect.
What would you expect from a sandbox that is not delivered by an AP, and how would you expect a published sandbox adventure to be laid out?
The introduction: How railroady is too railroady? Is it ok to open with a framing story like "You guys are on your way to meet King Soandso who as a secret task for you. You were intrigued so here you are," or is that too contrived? I guess I'm asking, what is the best way to get the players moving in a direction, any direction? In previous sandboxes players have complained that they simply didn't know what to do next.
Player vs monster level: This is much less of a problem in 5E than in 4E, but how do you plan appropriately balanced encounters in a sandbox when you don't know when or how players will tackle them? Or is this a feature of the sandbox, that players will run into things that can TPK them? Or that they'll run into encounters they can steamroll? I don't like the Oblivion/Skyrim "monsters are always your level" play that 4E pretty much required (or you were forced to run linear adventures, which is what I want to step away from), but I don't have an answer for the level disparity problem (if, indeed, it even is a problem).
The conclusion: When is a sandbox adventure over? My players are a big fan of free agency, but they are equally big fans of story, including the climax, the denouement, and the eventual end. But in a sandbox it seems like the ending is a lot more ambiguous, and more so the number of open threads you have going on. One thought I had was having all extant story threads funnel into one overarching epic, with all the foes they have fought along the way being pawns of one BBEG, but perhaps that's been done to death? Contrived? I don't know.
Player paralysis: With no big sign saying "go here, do this" my players are apt to scratch their heads and say, "I dunnow." And I by no means blame my players. I don't really think I'm that great of a DM, so I am either laying too subtle clues or I'm over-complicating my stories. I think it was Angry DM who once said to me on Twitter that even having a story (and I might be grossly oversimplifying or wildly misinterpreting what he meant) meant I was tacitly railroading my players. If that's the case, is player paralysis a function of their expectation that I have a trail for them to always follow? How do you instigate player action that more organically generates adventure?
Setting material: In no event has a player ever read any material I have ever written for an adventure. So is it a waste of my time? Is it still any good for internal consistency? Is internal consistency even necessary for player immersion? When you read a published campaign setting or sandbox adventure, do you as a DM actually read things like calendars, historical timelines, and exhaustive breakdowns of churches and factions? Do such things enhance sandboxes and where is the line that you've written too much?
You never eliminate railroading, EVER. You can only minimize it, keep whittling it down with experience. The key is to make sure your PC's have choices and options every step of the way. Be that during a combat encounter or roleplaying encounter, and if they make there own choice instead of using one of yours, even better.
Whether its a pre-written module or a "Sandbox" style campaign. There are still rails. To get from page 1 to the end of the book, gotta stay on the rails somehow to get to the end. If its a "Sandbox", well there is only so much sand, and the box is only so big.
None of this is a bad thing, it simply is what it is. You'll never eliminate railroading ever. But as a DM there are things you can do and techniques to use to ensure your PC's have as many options and choices as possible, and let the PC's feel that their actions help steer the world they are in in some fashion. IMO
That misses the point of the term "railroad " entirely and broadens it to the point of being meaningless. It's a metaphor. A railroad is a singular linear path. A sandbox by definition can't be a railroad and even an AP isn't necessarily a railroad. A good AP is closer to a highway system: you always start in Boston and you always end up in Washington DC, but there are lots of different routs with different scenery to get there.
Railroads can have more than one track and hiding the tracks doesn't take people off of them. If all rails lead to DC, that still precludes the underlying assumptions of a sandbox which allows for meaningful choices and multiple endpoints for a sandbox campaign.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.