I own a laptop and a desktop. I prefer the desktop, for a few reasons:
Desktops last longer than laptops. In Christmas 2014, I had gotten a new laptop and within 6 months of fairly average usage it broke. My family has a very old Desktop that my father got about ~15 years ago, its still in good condition, and can be used.
Desktops are more powerful than laptops. With the new desktop that I had gotten in Christmas 2015, so many new opportunities opened up for me(like Mario Party GCN netplay as an example), because it was so much more powerful and had a lot more RAM than my laptop.
The desktop has a bigger screen. Okay, this might be a bad reason, but I don't really care. Some applications were too big to fit entirely on my laptop's screen, and if I ended up not being able to resize it, I was screwed. With the desktop, I have a much bigger screen and the application window being to big hasn't been a problem for me on this yet.
And that's it. Laptops are portable, but portability doesn't really do much for me. I always used my laptop in my room, as I do with all of my handheld Nintendo systems. Anytime I tried to play a game outside of my room or use the laptop outside, I barely got any work done on my laptop, and I ended up always getting a headache while playing the portable games outside.