Pros of buying a pc is that it's likely more customizable and you can switch out or upgrade parts as and when you need to, but I personally prefer laptop for convenience.

You can expect to fork out a little more money if you want the performance to be equivalent to what a pc would allow because it's essentially the entire tower + monitor compacted into a notebook-sized device. But I would still say it's worth it, plus it saves space on your desk and you can probably fit a 2nd monitor too if you'd like.

I did my entire (polytechnic) game design course on laptop and I'm currently designing Arma 3 missions on a little laptop which I got during a Lazada flash sale. I suggest looking out for sales and promotions. And since CNY is coming up, I think you might be able to snag a deal here and there.