Can Gaming Laptops compete with Gaming Desk Top Computers?

Gaming laptops still fall behind desktops due to their power limits and cooling capabilities but that's not to say that gaming laptops are weak. They are still very strong computers. Laptops that are dedicated for gaming will almost always have their own dedicated GPUs nowadays. The laptops you're thinking about with APUs handling the graphics are mostly the lower end ones or ones dedicated more towards work related tasks.

The big difference between gaming laptop and desktop is power and cooling.  If you have the same gpu in both the desktop and laptop, the desktop model will be stronger able to pull more power and run hotter.

Gaming laptops often have dedicated graphics just like desktops. Although they are sometimes lower powered versions. 

If you are going to be putting many hours into gaming, i'd stay away from laptops. The heat will do numbers on components in the long run, and everything gets underclocked during use from the heat anyways. If it's just a bit of gaming for when you can't be at home on your desktop, they are amazing, but as the one and only machine to game on, i'd put more money into a desktop.

Although generally laptops can't fully compete, they are still pretty good. Portability is one of several good reasons to go with a laptop.

For  gaming desktop is better. Only advantage of laptop is portability. 

Any gaming laptop will have its own dedicated graphics cards. They just run into limitations with power and cooling compared to desktops. So while they are not as powerful as their desktop counterparts, they are still very capable machines and you can game comfortably. Just be prepared to pay a premium for the higher end machines compared to a desktop for the same performance.

I've always preferred desktops. In addition to what's been mentioned by others (cooling, power, etc), desktops can be updated with new components

https://www.youtube.com/watch?v=BQ4lx7_f4mk  Desktops

https://www.youtube.com/watch?v=Jr1cC7pyZME  Laptops

https://www.youtube.com/watch?v=33Tvwr3CSIc  Desktop vs laptop GPUs

Power and speed are kings.   Power causes heat as loss and has to be removed.   Requiring more power.   Speed is determined by circuit/chip size and material.   Both can use the same tech. so this is moot.   More power requires more size and a desktop-sized laptop isn't very portable.....

So do you want performance or portability?   

Gaming laptops are crazy powerful these days, and in most cases, will work great for most users. But desktops will always have more space for upgrades, better/more powerful hardware, and much more potential for "future proofing" (however futile that may be in the world of computers!). Laptops are a great option if you'd like the extra mobility, but if you're planning on staying put, a desktop will give you more options and flexibility into the future.