Which type is best? Of course, the answer is neither. It depends on what you prefer and need. If you ask on one of the modeling forums, a bunch of people will advise a gravity fed airbrush. So what are the differences? After using both for a while, I can tell you what I think.
Gravity fed airbrushes will do finer lines: Well, yes, but the difference is minor. My experience with the gravity fed Patriot and the siphon fed Anthem, which are really the same brush except for feed type, is that for me at least, with the same needle and tip size, the results are virtually the same. The gravity fed airbrush doesn't have to overcome the vacuum in the paint chamber to spray. But, when using a side cup, my experiments show that it doesn't really matter that much.
The main controlling factors are needle and tip dimensions. However, siphon fed airbrushes don't generally come with really fine needles and tips. If really fine lines are important to you, a gravity fed brush is the way to go.
Gravity fed airbrushes can spray with less pressure: Yes again. But again, it's not a big difference. The Anthem sprays fine at 15psi with a side cup, and the Patriot needs about 10.
Gravity fed airbrushes waste less paint: Maybe. Yes, you can put a couple of drops of paint in a gravity cup, and it will all spray except for the little bit that coats the inside of the brush and cup. With a siphon fed airbrush, you have the additional paint path of the siphon tube, plus whatever paint doesn't get sucked up. But, with the design of the Badger paint cups, almost nothing gets left in the cup or the tube. I can put 2 drops of paint in the cup, and most of it gets used. Plus, I've found that, with a gravity fed airbrush I have to pre-thin small amounts of paint before putting them in the cup, or they won't mix well. So that means using a separate mixing container, with some waste there. With a siphon cup, I can get a good mix right in the cup. So, I don't think this is a major advantage. One reason people might use more paint with a siphon fed airbrush is that this type usually comes with a larger nozzle. This makes it easier to spray a lot of paint, whereas with a smaller nozzle you might tend to be more careful.
Gravity fed airbrushes are easier to clean: A little, but we're talking less than a minute. Both types have a cup to clean. The only real addition is the siphon tube, and that just takes a quick swab with a pipe cleaner.
The cup on a gravity fed airbrush blocks the view: I noticed this when I first used the Patriot. But, you get used to it so fast, it isn't worth mentioning. With a little practice, you can tell where the paint is going to go.
The cup on a siphon fed airbrush gets in the way: Maybe. With a bottle, yes, but you don't normally use a bottle when you need to get in close. Maybe with the standard straight Badger cup it could be awkward, but the -483 cup with a curved stem tucks in under the brush, and is pretty much out of the way. I guess it depends on how you paint, so it could be a factor.
A gravity fed airbrush won't hold as much paint: Well DUH! The gravity cup is probably about 1/3 oz. and you can put a pretty big bottle on a siphon fed brush. No doubt this is an advantage if you paint large objects. But for most plastic models, this is not a major issue. 1/3 oz. will cover a pretty big area. Just don't forget the cap.
A gravity fed airbrush has faster response: This is something I read on one of the airbrush forums, and I admit I have seen it a bit when trying to do fine lines. Because of the longer paint path of the siphon fed brush, there is a little more hesitation when the trigger is pulled back before paint sprays. It's so minor that you have to look for it, but it is there.
My preference: I love my Patriot. It feels good in my hand and does a great job. But, if I could have only one airbrush, it would be my Anthem. It feels just as good and gives me the option of using a bottle if I need one, and wide coverage if I want it. And, with the choice of needles and tips, I can do lines just as fine as the Patriot. Which one I choose depends on what I'm doing. I keep the fine tip in the Patriot and the standard tip in the Anthem, but either one will cover most of my needs.
So I don't think it's that big of a deal. Consider the differences and decide what is important to you. People do excellent work with both types. It's really the hand on the trigger that matters.
Siphon Fed?
According to Wikipedia, a siphon is a tube that allows a liquid to flow over the edge of a container without external power as long as the exit end is lower than the surface of the source. My copy of Webster’s New World Dictionary agrees with Wikipedia. Anyone who has used a piece of tubing to drain an aquarium has seen this. If you raise the output end above the aquarium level, the flow stops. There is some disagreement as to whether this is due to atmospheric pressure difference or gravity, but the source is always higher than the exit.
Obviously, this isn’t what is happening in a siphon fed airbrush. The source, whether a cup or bottle is lower than the nozzle, and the liquid is drawn up by a vacuum. It is really a vacuum pump. It would probably be more correct to say the airbrush is bottom fed, and I have actually seen that term used occasionally. But, as long as you and I know what it really is, who cares?
There is also a biological use of the word siphon to mean a tube in general. But, an airbrush is not biological as far as I know.