IMHO, a sandbox is far easier to both set up and run than an adventure path.
A sandbox does require you to create a more detailed setting than an adventure path, but as it is extremely likely that your work will be visited more than once, the effort-to-reward ratio tends to be higher. For example, in one game I started with a local cave system (known as The Dragon's Lair, although there are no dragons there). Some time later, aware that they hadn't explored all of the area, the more powerful PCs returned. Similarly, in one 2e campaign with dozens of players, the Dungeon of Thale played a central (but not exclusive) role.
Most sandboxes start with something obvious, and then explodes into options. For example, PCs start at a village, and hear about some local caves. Exploring the caves brings up leads to two other possible adventures. Exploring any of those links to more possible adventures. And so on. And so on. In systems where statting is easier than 3e, the DM need produce only an outline to any given adventure, and then flesh in the details when (if) the players show interest. Starting a sandbox is as easy as picking a few adventures from Dungeon, placing them on a map, and then seeing how the various plots and places interact with the PCs. This might be even easier by picking some older modules (1e, BD&D) and their 3.X conversions. Or pick up the Wilderlands of High Fantasy boxed set....and "old school" sandbox setting if ever there was one.
The current model of D&D (soon to be replaced) makes sandbox DMing difficult in a couple of ways. The first is that statting out areas takes far too long. When prep is easier, then it is far easier to prep more (and hence a larger area). The second is that the rate of advancement, coupled with the power curve from advancement, acts to quickly make areas with appropriate challenges less than challenging. A 3.X DM fully prepping 3-5 areas for 1-3rd level play has very probably wasted 3-4 of them. 3.X, without modifying XP awards/level progression at least, is very unfriendly to sandbox DMing. By reducing XP to 1/2 (or even 1/4), 3.X becomes far easier/more fulfilling to sandbox.
The most important thing about creating a sandbox is that the world has to be interesting enough to capture the players' imaginations. And this is, perhaps, where some DMs find sandbox DMing to be "too difficult".
Here are some easy ways to relieve those problems:
(1) Whenever you create a significant part of the world, create a secret to go along with it. Remember this one from Dungeoncraft? It's perhaps the most important sandbox "secret" of all time.
(2) Interconnect. Say that you're starting a game using 5 low-level modules or Dungeon adventures in your starting area. Go through them, and find ways to refer to at least one of the other adventure areas in each area. Perhaps the villians are related. Perhaps one villian has sent an emissary to another. Perhaps there is a letter. Perhaps one area is gearing up for war against another. This doesn't have to be horribly sophisticated. For example, if you are planning on using The Last Dance, then the forest where that module takes place can border several adventure areas....and the DM can have the humanoids in those areas afraid of the "haunted forest".
(3) Expand. As you devise new areas, or add new modules/adventures, keep up the same process of interconnecting them. You can modify areas to do this, so long as the PCs haven't explored them yet. You should never say to the players, "From now on, we'll pretend that the ogre you met last week said....." as it breaks the illusion of seamlessness.
(4) Create foils. This doesn't just mean villians. It means rival adventurers, and rival adventuring parties. Some of them should be nominally "on the same side". Foils give urgency to the players; if they don't crack the Egg of Coot first, surely the Company of the Purple Feather will do so. Remember that foils are intended to spur the PCs on the greatness. This is where the DM should use his desire to create PCs. These people can be totally KEWL! -- showing the players what they can achieve. They can, and should, be able to outdo the PCs (at least in the beginning). They exist to be overcome, and grown beyond, though, so the DM should allow the players to measure their progress by hard-won victories over their foils. Earning the grudging respect of a foil...or making a foil into an ally...is a wonderful feeling!
(5) Create allies. For every foil you create, make 2-3 allies. Allies are characters who support, help, aid, and otherwise make PC lives nicer. They might be sages, wandering merchants, innkeepers, farmer's daughters....it doesn't matter. What matters is, if they charge, the cost is upfront. There are no strings attached. They are "good guys". Some of them can get PCs out of jams. They can offer advice and support. They cannot, however, generally fight the PCs battles for them. Most allies should be far less powerful than the PCs...at least by the time the PCs have a few levels under their belts.
Many DMs forget the importance of allies. Allies are characters that tell the players that they don't need to be completely cynical about the world. They are characters who offer safe haven. They grant role-playing opportunities. It is okay to threaten allies very occasionally, but if you use allies to pull strings at all frequently, the players are unlikely to get very close to them.
When the players go against the King, it is cool to have their ally, the King's Forrester, warn them about the foolishness of their actions, and say "If I can find you, be certain that so too can the King." It is not cool to have their ally lead the King's men to them, or assassinate them in their sleep, or be kidnapped by orcs at least once every game year.
The game works well if no more than 1 out of 10 "allies" turns out to be a foil in disguise, or if 1 out of 6 foils can be turned into an ally. You can use monsters as allies....the minotaur in the Labyrinth of Koss that acts as an oracle to those who pay it in horseflesh, for example, but few allies should "show up" the PCs. In general, the flashier the ally, the less mobile that ally should be. If you have to go to the Vale of Shadows to encounter Atlas, because he's busy holding up the world, that's better than an Elminster who can show up anywhere and outdo the PCs.
The Golden Rule is that allies are more important to the game than foils, but foils tend to be flashier than allies.
(6) Description, description, description. You don't need to name every orc, but it helps if you keep lists of names so that, if the players ask, every orc seems to be significant. When travelling, let the players know what the road is like, what the landscape is like. Lots of little streams? Markers on the road? Tell 'em! Toolbox is a useful...erm....toolbox for this sort of thing. The important thing is to let them feel like they live in a world that breathes, and exists without them. Mention normal animals...birds, squirrels, etc. ....so that the wizard's familiar spying on them one day doesn't stick out like a sore thumb.
FASA's Doctor Who RPG used the term "recognition handle" for some characteristic about PCs & NPCs that made them instantly recognizable. Think about what recognition handles you can give NPCs....and towns, and wilderness areas.
When you're reading a good novel, jot down bits of description that stir you. Mention things like a glint of sunlight off a far, lonely tor. The players might want to discover what it is. Even mentioning hills might make them want to know what's on the other side.
Good description stirs the imagination. Get yourself a mixing spoon.
(7) Take notes. If you make up a detail in one session, jot it down so that it is consistent going forward. If the two stablehands are Bob and Nob in one adventure, but their names chance to Fred and Bread in the next, the players are going to wonder what happened.
If you do end up making a mistake like this, though, try to roll with it. Come up with a reason why it makes sense, if you can. Make it a feature, not a bug.
Example: In one campaign, an NPC is named Octavia Augustus. The latin-teaching player asks, "Shouldn't that be Augusta?" Quick answer...No. Why? Because if you want to create an illusion of a living, breathing world, you need to be willing to pretend that Octavia Augustus existed before the players asked for a name. Afterwords, you can determine that OA is actually a male cross-dresser, and that the name is a clue.
(8) Pay attention to the players. If the players are interested in something, flesh it out more. "Flesh it out" doesn't mean "turn it into something fantastic or all-powerful". It just means add detail. If the players are interested in the history of the +1 sword they found, give it history....and tie it into an adventure location you have prepped!.
In a sandbox game, the players decide what to do. You can certainly attempt to garner their interest, however. Indeed, you must attempt to do so. That's your job as a DM.
RC