I've always found the lens comparison tool at DxO Mark helpful. There's definitely a learning curve to understanding what the charts and graphs mean as well as how to use the online tool to display specific data. Here I've set it up for the two lenses you mentioned. Another good review site for Canon lenses is The-Digital-Picture. Here is a test chart that compares the same two lenses at f/5.6 and with the zoom lens at 55mm. Which lens is displayed at any one time is indicated by the arrow in the middle and can be used to point at the other lens by mousing over it.
But beyond all of the test numbers, the biggest difference between the two lenses is the maximum aperture. The 18-55 is limited to f/5.6 and narrower at 50mm, the 50mm f/1.4 can open up to f/1.4, is equal to the zoom (at f/5.6) by around f/2 and is much sharper by the time it is at f/5.6. There are pictures you can take with the 50mm f/1.4 that are not possible with the other lens. As with any tool, a lens is only as capable as the person using it.
This portion of your Question raises several points that might be relevant.
† I'm at Panera bread, I shot a picture of my coffee cup 4 feet away with both lenses without a tripod on fast-shutter; both, pictures turned out identical to my naked eye.
It is impossible to judge an image based on what you see on the camera's LCD screen. An 18 MP image squeezed onto a 1MP screen can hide a lot of poor image quality. That screen will lie like a politician!
Apart from sharpness, there isn't a lot that will separate those two lenses at f/5.6. The value of the 50mm f/1.4 is the ability to open up the aperture and take photos that the other lens is not capable of. Besides the narrower Depth of Field, the wider aperture allows you to use faster shutter speeds in low light. Try that same experiment at the Panera Bread at night without a tripod!
Buying photo gear because everyone recommends a particular piece and without understanding why you need this lens over that lens is a good way to waste a lot of money. Instead of buying gear to try and improve your dissatisfaction with your photos, learn how to use the gear you already have until you bump up against the limits of that gear. Then you will know what you need that you don't already have, and understand what one piece of gear can allow you to do with a photograph that another piece of gear can not.
A boring snapshot of a coffee cup will look the same regardless of the gear used to capture it. To get impressive images, you must learn how to see the composition and the light and the possibilities of combining the two. That, more than the gear you use, will allow you to produce images that differentiate themselves to even the most casual observer.