What are the advantages of seasoned cast iron vs enameled cast iron?

Enameled and seasoned cast-iron cookware share a number of properties; they're very heavy, not terribly conductive of heat (leading to hot-spots when over a high flame), and capable of storing an enormous amount of heat energy. Cast iron itself is very reactive and tends to rust easily, which is why it is seasoned or enameled to protect the metal with a coating of either polymerised fat or fused glass, and these two processes lead to a number of differences:

Non-stick properties

Properly seasoned cast iron has a quite good non-stick finish - it won't be as smooth as a Teflon pan, but at the same time, the seasoning is much harder to scratch off and can be safely brought to searing temperatures that would cause the Teflon to begin breaking down and releasing toxic compounds. Enameled cookware, on the other hand, is about as non-stick as stainless steel, i.e. not at all non-stick. This means that many frying applications prefer seasoned cast iron over enameled, where getting a smooth release from the pan is important to the dish. For example, I'd much rather fry eggs in seasoned cast iron than enameled.

Setup & initial seasoning

Enameled cast iron is ready to go right out of the box; give it a rinse to remove the dust of storage and travel beforehand, but otherwise it's usable as is. For bare cast iron, and even the pre-seasoned stuff you often find nowadays, it's wise to put a couple layers of your own seasoning on it before cooking anything. This process has been described in many other places, so I won't repeat it here, but it involves washing off any protective coating from the factory before spreading a very thin layer of fat or oil over the entire surface of the pan before bringing it up to a high temperature on the stove or, for evenness, in the oven. Some people recommend flaxseed oil, but I would steer you away from it; the resultant seasoning has a tendency to flake off. Any fat with a high smoke point should do: vegetable, peanut, canola, coconut, even (relatively pure) lard.

Washing & storage

Seasoned cast iron has a reputation for fussy maintenance, and while it does take more respect and diligence than most pan materials and coatings, it's not as bad as it's sometimes made out to be. Maintaining seasoned cast iron involves not letting it stay wet after washing, avoiding particularly harsh detergents or abrasives in the washing process and, if it's not getting enough incidental seasoning from regular use, periodic manual re-seasoning. Meanwhile, enameled cast iron is coated in a layer of what is effectively glass, and it could not care less about your detergents or being allowed to air-dry. Scrubbing with literal steel wool might be a bit much, but anything you'd do to anything made of glass in the sink should be safe for enamel.

Reactivity

Some folks warn against using seasoned cast iron for acidic foods for the same reason they warn against aluminium; the acid in, say a tomato sauce, or Filipino adobo, can leach metal out of the pan and into the sauce. In iron, at least, this can be either good or bad for you, depending on your iron levels otherwise - nutrition isn't on topic here, so speak to a doctor if you're concerned. A heavier layer of seasoning, less liquid foods, and less acidic foods are all ways to minimise this effect. Enameled cookware, meanwhile, is still covered in a layer of nonreactive glass, and won't exchange anything but heat with the food you're cooking.

High heat

Cast iron is often held to be an ideal material for searing food in; its respectable specific heat capacity and very high mass give it an enormous amount of thermal mass, meaning the temperature of the pan won't drop too sharply when food is added, and giving it time to pre-heat for searing can even out the hot-spots caused by its middling-to-poor conductivity. Of the two varieties of cast iron in this question, seasoned can take a somewhat higher temperature that enameled; while it is possible to burn off the seasoning layer, it takes a higher heat than damaging the finish on an enameled pan. This isn't a huge difference, but it does exist. One thing to note is that if your pan or pot has plastic or other non-heat-proof handles, removing these can leave you with a pan usable in a much hotter oven. Indeed, some companies manufacture and sell heat-proof knobs and handles for their products to replace the default ones.

Overall, while both varieties can be used quite well for both frying and stewing operations, the properties of seasoned cast iron lean it towards those frying and searing applications, while enamel is geared towards stewing and braising. This is why it's so much more common to find a seasoned cast iron skillet and an enameled dutch oven than the reverse; the opposites do exist, but they're much less common.

Incidentally, I'd be somewhat skeptical of a cast iron pan sold as a paella pan; my understanding of paella pans is that they're typically thin, light, and made of stainless steel. It's entirely possible that what they're selling as a paella pan is a perfectly reasonably cooking vessel, but I don't know that it's what you'd want to make paella in.