There is absolutely nothing wrong with the 1.8. Its a fantastic lens. The 1.2L glass is unmatched but honestly, if it doesn't match your budget it's not worth going into debt for.
You'll get amazing image quality with the 1.8 and if you can notice a difference between that and 1.2 you're a depth of field genius. LOL. I can't see where you'd go wrong buying the 1.8.
Good luck.
Theoretically, a faster lens of the same focal length should be softer. Perhaps not much softer but a little. An 85mm f1.2 would be a specialty lens for low light photography or extremely narrow depth of field. It shouldn't provide better image quality assuming similar quality.
I own both the 1.8 and the 1.2. They are two different pieces of glass with two distinctly different purposes. The 1.8 is fast glass with fast focus and an nice quality to the background blur. It is a great all around lens. It is one of my goto lenses for indoor sports.
The 1.2 on the other hand is very much a portrait lens. I doubt I have ever shot it wide open. I didn't buy it for the low light capabilities. I bought it for portrait work. The quality of the background blur is second to none. It produces the kind of bokeh that most people strive for in portraits. Only my 300 f2.8 and 400 f2.8 give me the same quality of bokeh and both are a little inconvenient for studio portrait work. The focus speed is average, not on par with the 1.8 but then that particular point does not matter to me.
Both are excellent lenses for their particular purpose.