[I can't sleep, so I guess I'll wade in these waters...]
There are a number of things that separate the work of the working pros from the rest. Here are my $.02, with the most important things on top:
Purpose
Pros have assignments - either given to them or given to themselves. Sometimes they are mundane - photograph the opening of a new store, photograph a new car, etc... And sometimes they are not - cover a war, cover a speech by a noteworthy politician, go to a remote wilderness and capture epic sunrises/sunsets/etc. Guess which ones make it into print and into their portfolios?
When they go on these assignments, that's their sole purpose. They're not going with the family and trying to sneak in some photography. They're not going to the local park for a walk and hoping to stumble upon an epic shot. Can you get a really nice photo this way? Yes. Can you get a great photo? Not consistently, and you often need some luck/good fortune.
Practice
There was a study a number of years ago that concluded that the key difference between a very good athlete (i.e., college-level) and an outstanding athlete (i.e., Olympian) is simply hours spent practicing. Olympians start training their bodies at a ridiculously young age (some as soon as they begin to walk) while folks that peak at the college-level started getting serious about sports at a much later age, i.e., 9 years old. Those handful of years (and hundreds if not thousands of hours of practice) gives the Olympians a tremendous advantage.
I think photography is much the same way. We've all heard about the Rule of Thirds, shutter should be 1/FL, and other nuggets of conventional photographic wisdom, but who's going to code that into their synapses faster and more deeply - the pro that's shooting and critically evaluating hundreds if not thousands of shots a day, or the weekend photographer? And when the decisive moment flashes in front of you, who's going draw from that knowledge instinctively vs. consciously?
Post Processing
Every single photo in a good magazine is post processed by very talented people that do this stuff 30 hours a week or more. They know their tools. They know their medium. Every single photo in a pro photographer's portfolio is processed by people whose paycheck depends on knowing what they are doing. The rest of us post stuff online - some of it SOOC, some of it PPed a bit (a tone curve here, a slider there, done), and some of it PP'ed extensively. There are some gems in there, but they are buried in a sea of mediocrity/gear tests. No wonder our stuff doesn't measure up.
Gear
Of all the things on this list, gear is the least important. It's not unimportant, particularly in situations with challenging light. But we've got to admit that we're in a golden age when you can buy a 24Mp camera that shoots a nice ISO3200 with very good exposure range along with a kit lens and a 50/1.8 and 35/1.8 and still be under $1000. All this fussing about an extra stop of ISO or thinner DOF of larger sensors is way way way less important that the stuff above.
Personally, my photography took a big leap forward when I started shooting with a purpose, volunteering for an NGO and local non-profits, choosing to photograph the campaign of a local politician, going to Zuccoti Park with the sole purpose of photographing what was happening, and motorcycle travel photography for RoadRUNNER Magazine. I ended up with a ton of photos that I could look at critically, and really hard-wire some key photographic principles and ideas into my brain. I've gotten better at post processing too, but I know that there's a ways to go still. And I'm still fascinated by gear, but now decisions are made with regard to a purpose - the kinds of projects I see on the horizon - not just simple measurebation.
So to answer the OP, it's neither gear or PP.
Good night and good luck.