This question has always been going around and I always look at what people purchase. Recently a lot of the laptops have become more powerful so they use their laptops as desktop replacements. Personally I prefer a desktop for home and laptop for mobility so I have both, but some people have one and stick to it.
The good part about these new laptops is that you can pretty much do anything on them without any issues, and they can handle what you throw at them. The advantage of a desktop is that you can upgrade parts cheaply and it will become powerful with just a few different parts. Also prices for both types of machines have dropped a lot recently and you can get a powerful machine for a low price.