Assuming you're referring to a manned landing,
The question lies in HOW they choose to get there, in my opinion.
During the Cold War, both the US and USSR pursued "single launch to moon" designs in which an orbiter, lunar lander, and associated support systems were to be launched in a single vehicle and propelled to the moon with no further assistance. "Assembly in orbit" systems in which several segments would be launched individually, connected, and then launched out of LEO were considered but ultimately disregarded because (if I remember correctly) at the time the mechanics of sending up a first module and maintaining it in orbit while a second launch could be prepared for some time weeks or months down the line were considered "to complicated" and time-consuming compared to simply building a bigger rocket.
Now, however, the largest rockets are built for significantly smaller payloads. Comparing some current common launch vehicles to the Saturn V (260,000 pounds / 120,000 kg to LEO) and Soviet N1 (200,000 lb / 90,000 kg to LEO), we see:
Atlas V - 64,820 lb / 29,400 kg to LEO
Delta IV - 49,740 lb / 22,560 kg
Long March 4 - 9,300 lb / 4,200 kg
Proton-M - 49,000 lb / 22,000 kg
Liberty (planned) - 44,500 lb / 22,000 kg
Falcon Heavy (planned) - 120,000 lb / 53,000 kg
(numbers snagged from Wikipedia)
All the rockets today carry a mere fraction of the payload that did or were expected to get us to the moon. This leaves two options: Assemble something in orbit, or build a bigger rocket (again). The US seems to be leaning towards the latter option with the descriptively-named Space Launch System, which will even surpass the carrying capacity of the Saturn V. Frankly, though, I think most of the private companies will go for the "build it in orbit" idea.
First off, we're a LOT better at putting things in orbit and keeping them there than we were during the Space Race; there are several generations of engineers who participated in the Skylab, Salyut, Mir, and ISS programs - the latter two being particularly significant as they also involved building things in orbit which didn't even always come from the same country of origin.
Second, computers are a lot better today. While I'm not a electronics engineer or computer scientist, I'd be surprised if we couldn't rely on computer systems to mate two unmanned components safely. Compare this to the theoretical "build it in orbit" ideas from the space race, where humans had to be part of the immediate docking process - in turn, forcing you to either resupply them, recover and then relaunch a crew later, or be ready to head out as soon as docking was complete.
Finally, I'd dare say that some of these companies - SpaceX in particular - would love the PR they'd get from building something in orbit, particularly as it pertains to SpaceX's stated goals of expanding the human presence in the solar system.