I'm a fan of Desktop. I'm not a gamer however I use it for chess study and practice, social networks, music and movies. The fact that you can tweak specific components is a big plus for me.
A laptop is convenient for its mobility. But I'd choose a desktop because I can get monitors as big as I would like. With a desktop, I don't have to worry about maintaining the battery life. So Desktop all the way.
I prefer my desktop to a laptop, for any work on the go, I use my smartphone and cloud services. Laptop uncomfortable to carry and always more at risk to get stolen.