Well, it depends on the experience you're going for.
If you want a more social, hang out and play games with your buddies kind of experience, go for the PS4. It'll also be a fair bit cheaper than going Alienware, and a bit cheaper than a gaming PC you would build yourself.
If you want a no hassle experience, go with Alienware. If you have the budget, you can get quite a powerful machine and turn all the eye candy up to 11. While you can't hang out on a couch with your alienware as well as you can with a PS4, I've found plenty of opportunities to socialize with PC gaming (Teamspeak with my friends, that kind of thing). The main point of going for a PC like this would be to take advantage of the superior graphics. Games will look
much better on a gaming PC than on the PS4.
Finally, if you're willing to get a bit adventurous, want to settle for nothing but the best, and are willing to learn a little, building your own PC would be the route to go. You'll get the best performance for your dollar, and if you pick the parts right, a
very reliable machine. This option gets my personal recommendation. Building your own PC is pretty simple: think Lego. And it's a very rewarding experience. Plus, it's just badass to be able to say "I built my own gaming computer"
What kind of a budget do you have?