Yes desktops are more customizable and can be added more features, they are more stable as well since they have much space to breathe with, but thats just if your going to replace a home computer and that you'd let others on it(unless its in your room). i think laptops are more private and can also be useful since you can transport them.
i wouldent recommended a desktop unless your a hardcore gamer. and if you want to get your FPS higher you need to get a better graphic card, FPS is all about the graphic card, and like i said you dont really need super powerful computer for it to be better. i still recommend a 500$ laptop.