Well unless you're using a gaming laptop you're pretty much going to be in for a lot of disappointment, for the same reason that an xbox one isn't mobile a laptop won't be too good for gaming. And if you purchase a gaming PC it's highly unlikely there will be compatibility issues with certain games but over time your hardware might not be able to run the latest games at Ultra settings and maintain 60-80+ FPS. Luckily you can of course turn the settings down or use custom settings and just turn the AA or texture quality down a notch.
Depends how you look at it. As time goes on console games have to be optimised more and more and beautiful games have to be lowered in detail and texture quality to run smoothly, something we've seen recently with GTA V. This is because a console has a certain lifetime before the next console comes out and you can upgrade. On PC you can choose when to upgrade and it's usually a matter of upgrading a specific component. What I'm saying is basically you're paying for longevity not quality.
However how many people do you know that own a console but not a laptop or computer? Combine the prices of both purchases and you're talking about spending £600-800 on something that can do everything. Not just gaming, or just work/internet/audio & video editing but one for all of that for the combined price. I just ordered a custom built PC that'll be able to run the newest games for years to come without breaking a sweat for the top end of that budget, and you can save money by going pre built. And anyone that doesn't have the know how only needs to talk to customer service reps and tell them what they'll be using it for and their budget and they'll be sorted out.
If you use Steam then you know how easy it is too, and like I said previously about loss of quality for longevity on consoles compared to both on PC. Also in regards to Steam, the prices for games seem fairer on PC. And less of the DLC ripoffs that we've being seeing lately.