If you want my absolute honest opinion, absolutely not. It is miles and miles better than the PS4 controller IMO and I have never heard of these problems that you have been having with your controller. Sorry I can't be of any help to your situation or offer any insight, but I am just throwing my two cents out there. 

Yep. Happens with every controller, but not for every game. In fact, it only effects Halo 3 (360) and funnily enough Halo 3 on xbox one.

If its not gamebreaking, I'm sure you can deal with it.

Hey, I like the Xbox One controller more than the PS4 controller, too! To this day, I can't figure out the complaints it was getting back during launch.  The thing is fantastic (AA batteries, aside--though I use rechargeable batteries that last forever!). The drift issue is aggravating, though. I like all of my consoles but if I see something wrong, I call it out. Nobody gets a free pass!

My old PS4 controller started doing that, but that was after server wear and tear.

It's a pretty common problem ever since the days of the Xbox 360. One time I decided to analyze it a little further, because it really got onto my nerves. It just makes gaming so less precise. So I hooked the controller up onto my Linux PC with some neat little tools to analyze just about anything. Turns out that ALL of my Xbox 360 Controllers were jumping all over the place when I didn't touch the analog sticks. Both X and Y axis were jumping back and forth between 20 and -20. It's a problem that could be fixed with a customizable dead zone. I don't know why they haven't included that.

The DualShock 4 tends to have similar issues, though not quite as bad. It can still be noticable though. However, no controller ever will beat the good ol DS3 in that regard. That sucker showed me a whopping 14 axes (because the action buttons were analog n stuff) and ALL of them were rock solid at +/-0 on all my controllers. Sony really went all out with that one. In this new gen, they started to save costs I guess. That's why I'm still using the DS3 on my PC.

For your everyday experience it shouldn't be too bad though, neither with Xbox One nor PS4. The only time you will really notice it is when you get competitive in gaming and every pixel counts. But in that case, you probably will get a better controller anyway, like the Elite Pad for the Xbox One. I haven't tried out that one yet, but I would be seriously disappointed if that thing has the same issues.

There definitely is an issue. The controller that came with my system started drifting on the right analog. I look at the analog stick and it's perfectly centered so it might be something internally. Either way I'm pissed I had to dish out $65 for another controller.

I have that problem with a Xbox 360 controller that is almost 10 years old.

Would I have to replace the analog stick module or the thumbstick cap? Or maybe just cleaning?

EDIT: I just opened it and yeah, there is dirt. I'll report later if it worked.

EDIT2: Yeah, it worked.

OK, we have a point of agreement then! 

Well I found the hard way that chatting with people in party chat and taking cookies out of the oven do not mix well. I ended up snagging the mic cord on an edge while putting some cookies in the oven and the controller went flying into the oven (one of the thumbsticks was in the back of the oven for almost five minutes before I could fish it out).

That somehow gives crisp party chat a totally new meaning.