I’m not sure what you mean here. AirDrop is for transferring bytes from one computer to another. There is no such thing as moving data between computers. There can only ever be copying between computers. I suppose you could simulate moving something by deleting the project from one of the machines after a successfully copy, but frankly I don’t see the point in that. You might as well have two copies around in case one computer melts down.
That’s up to you, it depends on what you are attempting to accomplish. If you wish to have a complete repository of your work on both computers so as to have a redundant store, then sure, copy everything over. If you just want to grab some work for the coffeehouse on your way out the door, then copying every single project you’ve ever worked on up to five versions in depth might be overkill. 
I feel like you might be asking something else though and I’m not parsing what you mean.
You won’t lose anything by copying files. Unless you overwrite files when copying, but even that can be safe if you know why and what you are overwriting.
Perhaps you’re thinking of this as being more complicated than it really is? The way Scrivener works is really no different than the way most other programs work. If you edit a .doc file on Computer B, and want to work on Computer A, you copy the .doc file to Computer A. When you get back home you copy the new updated .doc file back to Computer B. That’s all you need to do, and most of what needs to be done is just common sense. You don’t overwrite Computer A’s copy with the old Computer B copy when you get home—you update Computer B with the latest updates. It wouldn’t be any different with Scrivener.
If all you want to do is copy files between computers, AirDrop is probably better. Anything that requires the use of the Internet to function is going to be less secure than something that uses your home network exclusively (though, do be sure your wireless network is password encrypted, otherwise you are publicly broadcasting everything you do like a radio station!). On top of that, anything that uses the Internet to transfer data to some other entities computers and stores your data on machines you do not control or own is going to be less secure than only storing data on equipment you own.
To be clear, again, I’m speaking relatively as in my cable vs. air example above. Using Internet storage is inherently less secure than managing your own network, but in the grand scheme of things it’s pretty safe if you make the right choices! Dropbox isn’t bad, SpiderOak is probably better for security, but I wouldn’t call Dropbox security “weak”; that would be a bit hyperbolic.
So you are correct, AirDrop is safer and entirely controlled by you. Every bit you send with it stays in your control (granted, any time you broadcast bits over radio frequencies you lose control of them—but that is why you need to use an encrypted home network so that the broadcast data is scrambled).
Sorry if some of this is overly technical. Just think of Scrivener projects as files because that is what they effectively are. True, they are folders in disguise and all that, but a lot of the stuff on your Mac that looks like files are folders in disguise, so for everyday usage that isn’t something to worry about. Zip files work better over a network because they are optimised. For the same reason they take up less space on your computer—they are better for wireless broadcast. If you want to use the last .zip file that is created by Scrivener when you shut down the project—that’s great—that’s how I work myself. You can copy your whole backup folder each time if you want to take the time to do so—that’s fine too and you’ll certainly have better data redundancy. Personally I’d call it overkill, but you could do that, it won’t hurt anything but it might make things a little confusing with all of those dozens of versions laying around.
