Definitely a data problem at your end.
I watch Netflix on my phone all the time and it works flawlessly. (AT&T)
We've had LTE rolling out in my area, so I get an LTE connection about 60-70% of the time now, when I have that, it's fast and crystal clear just like on my television or WiFi connection. Actually I've had so many problems with Comcast lately, I've actually been using the phone to watch a Netflix show before bed some nights. My LTE connection is faster and more reliable than my Comcast home internet, kind of pathetic.
If I'm on HSPA+ it's still not bad, maybe just a bit of graininess as the movie queues up and gets loaded into cache or whatever, but I haven't had a movie pause to catch up or lose significant quality yet.
Youtube works well the few times that I use it. But youtube has it's own issues. Even on my computer with a very fast connection at work sometimes it lags. That's just youtube being youtube.
This definitely has absolutely nothing to do with how many cores your processor has. Any smartphone made in the last 5 years with a decent processor and a reasonable amount of RAM can stream video smoothly. Anything outside of that is a data connection/performance issue IMO.