Both camera's are ridiculously good, neither will make you a better photographer..
What you have to do is ask yourself is what kind of photographer you are and then base your decision on the camera that has the most pro's for your work.
What makes a great photograph is "light and composition"... unfortunately, they don't come with the camera.
I don't think I'v actually come across anyone yet who actually believes buying a camera, equates to buying photographic skill, yet I see this silly phrase banded around by people who are noobs themselves.
Can you buy better quality pictures.. Yes. For example it should be obvious a natural light portrait will likely look better (to most) on a wide open prime than at 5.6 on a kit lens.
A low light portrait, will likely look better on a 5d3 than a 10d. Obvious is obvious.
Note:
The above assumes the photographer meets the minimum threshold of being able to point aim and click.
Your second sentence (from the first quote) however makes sense but is redundant, as I think it's clear that is actually what the Op is already trying to do.
There are so many stupid comments about sharpness of lenses and how one manufacturer is better than the other.. I could pick 2 fantastic pictures off of 500px and ask you to tell me the camera used and guarantee no one could tell one from another.
Especially at web res.. **bangs head against wall**
I've seen pictures taken with the nifty fifty that are outstanding, I've also seen people who own £20,000 worth of camera equipment and don't understand the relationship between shutter speed, aperture and ISO...using AV all the time!..
Firstly.. who was this person, what camera gear were they using and were they new to photography?
Secondly it's not really that taxing to understand the exposure triangle. It's something I could teach someone in a short time.
I started off similar to you. Shooting full manual, feeling proud of myself that could control every aspect of the exposure. Setting my base ISO, choosing my aperture for the required DOF, dialing in the shutter speed to control the ambient, upping the flash power until I was happy with the overall exposure. I can still hear Zach Arias in my head repeating "Aperture controls flash exposure".
Time moves on and tastes change. Now I'm shooting natural light in Av + Auto ISO 95%. I can't remember the last time I shot full manual, it's hardly necessary for everyone.
In essence what I am saying is it really does not matter, not one iota..
Huh? but in your 2nd sentence in the first quote you said...
Do you actually even practice what you preach, are you running around with entry gear because your enlightened and know it doesn't matter one iota?
No.. your shooting with a 5D3!
Why?
Looking at your flickr, you have control of light (flash) so you don't need good ISO. Your not shooting shallow DOF's, so don't need the added control of DOF that FF brings. Nor do you need a fancy AF system.
In fact you pretty much don't need anything special that the 5D3 brings to the table over a 550D + Nifty Fifty.
Do you not see the irony here?
What happened.. did you mistakenly buy a 5D3 thinking it was going to make you a better photographer?