Fountain pens can take on ink either from a bottle or a cartridge. The vast majority of high end or vintage fountain pens use only the bottle, drawing ink into the pen through the nib. Most low-to-medium end pens take ink from either a cartridge, or a converter that allows the use of a bottle. Both options have advantages and disadvantages.

Bottles of ink are just what they sound like: a glass jar of ink. Typically they have about two ounces of ink. Some have a pocket inside to make filling easier as the bottle starts to empty. Glass is used, as plastic is porous, causing the water in the ink to evaporate, leaving just a dense concentration of the dye that gives the ink color.

Cartridges are purchased from the manufacturer full of ink, and sealed. Inserting the "cart" into the pen breaks the seal, and ink flows.

A converter ships without ink, and is inserted into the pen. Then, the nib is put into a bottle of ink, and some mechanism is used to draw the ink into it. Typically, it is either a piston (my preference) or a bladder that is compressed and released, creating a vacuum.

The principal advantage of the cartridge is convenience. There is no mess, bottles of ink, or cleaning after the the pen is filled (typically wiping the nib). Also, extra cartridges can be carried quite easily on a trip. In fact, most Cross pens (save for the Matrix) can hold two of their cartridges (one in use the other as backup) internally.

Cartridges have a few disadvantages. Many pens have proprietary cartridges, so they are only available from the manufacturer. There is an "international" cartridge (Waterman, Cross and Lamy use them). This is less of an availability issue (most major brands can be found at Staples or the like) than a flexibility issue. If the manufacturer doesn't make the color you want (or you don't like their ink for some reason), you are out of luck. Fountain pen collectors tend to obsess over the ink they put in their pens

Also, relative to bottled ink, cartridges are more expensive. A card with five cartridges may run $5; a bottle (which holds about ten "cards" worth) is about $10.

Some people get around the flexibility and cost disadvantages of the cartridge by using a syringe to refill an empty cartridge. While that gets the job done, it strikes me as defeating the purpose of the cartridge. You still have the mess potential of a bottle, and, with the seal already broken, they aren't really transportable. Unless the pen simply cannot take a converter (Cross Matrix, I'm looking at you), I wouldn't use this method.

The key advantage of the bottled ink is choice. You can use whatever ink you want in your pen, so long as it is designed for fountain pens (metallic ink, scented ink, and india ink are not suited for use in fountain pens). There are even some companies that only make ink, producing some dramatic or unique colors.

Also, you can pull water into the pen, to clean the feed. This should be done periodically, as well as when you change colors. Use just water--no detergent. Cartridges do not offer this option.

There is an intangible benefit to using a bottled ink. You get a retro feel by pulling ink from a bottle, they way the did when fountain pens were really the only game in town. It is the continuation of a tradition, as well as taking a more active role in the use of your pen. I think of it as the difference between buying a bag of Folgers a the grocery store, and buying just the beans at your local roaster, and grinding them yourself.

I feel that bottle-fillers and converters work better than carts. Maybe because the act of filling primes the feed. Or perhaps that there is not that bit of plastic still in the cartridge after the seal is broken getting in the way.

There are some disadvantages to the use of bottled ink. First, there is the mess. When dealing with the bottle of ink, there is the obvious potential for knocking it over and spilling ink everywhere. Even if you avoid that, there seem to be occasional drips of ink here and there. I seem to discover these when I rest a moist hand on my desk, then lift it up to a surprise. No matter how careful you are, you still have to blot the ink off the nip after filling. In almost ten years of collecting fountain pens, I've managed every one of these scenarios.

Also, bringing a spare ink supply along is much more cumbersome than with a cartridge. Either the whole bottle has to be brought along, or a travelling ink pot. Either way, there is an increased chance of a mess, and another thing to drag along.

Finally, though the bottles seal up OK, problems develop with old ink. As noted earlier, water in the ink can evaporate out, leaving a concentration of the dye. This can clog the pen. Also, mold can grow in the ink. How long this takes depends on the ink, the bottle, and the conditions it was stored in. There are some collectors who only use ink from the fifties.

Generally, you don't have to make a choice. The vast majority of pens produced today use a cartridge/converter system. Use the converter for most of the time, but have a cart on hand for an emergency. I even keep an Altoids box at my office with various cartridges for when I run out of ink.

Among collectors, bottle-fill only pens are held in the highest esteem, followed by the use of the converter, and finally the cartridge. All are seen as preferable to using a ballpoint pen.

Please note that almost all manufacturers of fountain pens put in a statement that their pens are engineered to work only with their ink. This is seen by most as either a way to sell more ink, or a legal disclaimer, in case someone tries to use India ink or paint or blood or some other thing not suited for a fountain pen. Though I personally do not match ink to pen, I recommend that you look at the instructions that came with your pen, and use your better judgement. I do not take responsibility for any problems that may arise from not matching ink to pen.

Sources:
The Zoss Pen list: http://www.zoss.com
Bottles of ink on my desk