Hi,

Gaming PC Straight Away.
Don't look at the portability factor. You need a proper GPU and a Proper FPS. Real Gamer Doesn't wait for graphics conversion from CPU to GPU.
You Should opt for a Gaming PC. Stability matters.
I have a Gaming Laptop and a Gaming PC as well. My Laptop Graphics specs is much high than the PC. But my PCs performance is much much better than the Laptop.

The rest is up to you

I would always go for gaming laptops. As these are easy to carry around. You Just need to have a Study table in order to enjoy the best gaming experience.
When it comes to gaming laptops, My first option would be Alienware 15 or 17(depends on your budget) because of the brand value associated with gaming. The second choice would be MSI laptops.
Alienware 15 Configuration :- 32GB RAM, 1TB HDD+ 1TB SSD + Windows 10 + 8GB Graphic Card.( What more you want.. )
Similar Configuration in MSI laptops cost lesser as compared to Alienware.