What advantages does a brasing pan have over a full Dutch/French oven?
I have this shape (without lid) as a cast iron pan, not enameled. I mainly use it in the oven, not on stovetop. 

It's a great pan for gyvetch, moussaka and generally Middle eastern oven dishes. You can brown the meat and sweat the onions in it on stovetop, then add the other ingredients and put it in the oven. All the juices stay in the pan - if you brown in a frying pan and then transfer to a ceramic pan for the oven, you lose some juices even with good deglazing, and it's logistically simpler to continue in the same pan. Also, the stovetop browning preheats the pan, saving time and energy. 

When it is in the oven, it has the advantage  that the hot air moves freely over the surface of the food, so you get the benefits of convection. The Dutch oven's high walls prevent that. Also, as Joe said, you could theoretically fit two of them in the oven at once. 

I also find it great for baking bread, its thermal mass gives it a function similar to a bread stone. When it is used open, it doesn't give you the pseudo-steaming advantage of baking in a closed Dutch oven, but on the other hand, it produces a nicer shape than a Dutch oven. 

For stovetop, it can double as a paella pan. It can also be used as a substitute for other pans - especially if unenameled, because it's nice to have something which can withstand scorching temperatures but is larger than a steak pan. It can even double as a wok in a pinch. But these are side benefits. You can probably use a large Dutch oven for the same purposes anyway. 

If you don't do much of Balkan or Middle Eastern cooking, it's not so important to have one of those. Especially as a cooking beginner you can find other equipment with higher ROI. If you are looking at those just because you noticed them in the shop, have the money, and want to enjoy your new hobby - I understand you, because I used to be in the same position. My advice: don't start with the gear. Start with a few simple, cheap items, and dive headfirst into cooking. When you find that your success with a recipe is hobbled by missing gear (as opposed to your skill, bad ingredients, etc.) and that you make this food style frequently enough, that's the time to invest in high quality items.