Both Laptop and PC have their advantages and disadvantages.
A laptop has portability, and an all-in-one setup is always convenient. But it's hindered by the inability to upgrade its parts easily. There are ways to get around this nowadays, like with an external PCI-e adapter allowing you to plug in a desktop video card. But the more peripherals you use, the clunkier your setup becomes. Another thing to keep in mind is battery usage.
A PC allows you to upgrade any part you want (which is especially handy, if a RAM stick dies for instance), and building one lets you know exactly what is going inside it, but as you said it isn't portable. They can also run rather large, and there will be a LOT of cable management to do.
You should get what works best for you ^^ Both are perfectly valid and capable systems for gaming. As long as you enjoy games, and have the ability to play them, what you play on shouldn't matter.