BDodd is the only one that has given any valuable information so far. He is a little off on one point, air movement will affect both types of weighing devices. It all depends on their sensitivity. The more sensitive the device, the more it is affected by air current.
A Beam Balance is affected more than a digital when it comes to the surface. The scale/balance must be on a level surface. Both types must be re-zeroed (tared) when moved.
One more thing that very few think about is vibration. Vibration is horrible on a balance, but less on a scale. Mounting your scale/balance on the same bench as your reloader is not a good idea, but most do it for convenience.
All you guys that say, "My X is more accurate", do you even know what it means to be accurate? If you think your scale/balance is accurate, why do you think that? Because you checked it against another scale/balance? How do you know that one isn't out of tolerance?
I spent 22 years as a Metrologist. I've calibrated hundreds of balances in that time. In order to say, with any veracity, that one is better than another, you should first know how they work.
There is a difference between a balance and a scale. A balance is just that, it balances two weights on a pivot point. In the case of a powder balance, the balance is obtained with arms of unequal length. This adds sensitivity, not precision, to the balance. The ability of the device to be precise depends on the design and quality of components. If you can avoid it, a balance should never be moved. The pivot point is called a "knife edge" because it's very sharp. It's made that way to reduce the friction applied to the beam. Over time, the knife edge will become rounded and the balance will become less repeatable (notice I didn't say less accurate, there's a difference). Every time you move the balance, you risk damaging the knife edge. If you ship a balance without creating a separation between the beam and knife edge, you will probably ruin the balance.
Most digital powder weighing devices are scales. A scale uses a spring or load cell to push back against the unknown mass. In the case of a digital powder scale it has a sensitive load cell, or transducer, that creates a voltage relative to the amount it is compressed. These load cells are very robust and vibration tolerant. In an environment where the scale will be moved a lot, the digital is much better than a balance. There are no knife edges to worry about.
Be wary of cheap digital scales. They are not very repeatable due to load cells that are cheaply made. Thus they need to be tared every few minutes. Also, it is a good idea to allow your digital scale to warm up. Turn it on and let it sit for about 1/2 hour. This allows the voltage in the load cell to settle. You will find it works much better this way.
I never recommend battery operated scales. They don't stay on long enough to properly warm up. Yeah, they work, but they are not the best solution.
I do recommend digital scales for reloading shot shells. They are the easiest to maintain and fastest to use. Did you know that a balance should be read while the beam is still moving? This reduces the affects of stiction on the measurement. This is why a digital is better for the home reloader. You just pour the powder on there, wait for the stabilized light to tell you it's not changing and you're done. You can also move the digital around without worrying about damaging it.
Balances are fine and just as accurate as the digitals. The digital is just more practical and reliable for reloading.
If you've read this far, you have enough information to go out and buy a scale or balance to suit your needs. This is not the area to skimp in. Get the beast measuring device you can afford. If all you can afford is a $25 scale, then reloading is not for you.