Well there is a wide range of quality but to be frank, IMHO it goes something like this:
(this from my own experience, maybe I was lucky or unlucky)

~3% {+-2%} Really really good ones, excellent stories comparable to reads from professionals writers and usually as good story as the one from which it originated (I also found one that was better but the source from which it drew on was just above average ) Here usually there is also excellent writing, spelling, grammar and format. (Well by default in fanfiction you can't expect everything to be flawless even with beta. There is a large percentile of writers that English isn't their primary language). Many original plots and interesting twists on them or existing ones (found also on other stories) and smartly written... I could go on but, to be short, these are stories that it is my belief could be published (if there weren't fanfiction that is).

~7%{+-5%} Good ones, you will appreciate them, many of them maybe as much as the original, and it's a nice little escapade from the real word and/or from the source's world (If it's a very AR story). Highly enjoyable. Also original themes but mostly there are usual themes that are found also on other stories of the same category but there original twists and/or are written really good so you will enjoy them nonetheless. The same reason you will read a fantasy story with a similar setting and story you have read in another book. Just because you have read LOTR doesn't mean I will never read another fantasy book with dwarfs epic wars and wizards again, right? I also found stories in this percentile that was my belief that they could be published. (Not all published books are the same quality). Usually minor errors in spelling and grammar.

~15{+-5%} So-so to decent ones. They are okay. You will most likely enjoy them but most often than not you will read them in a hurry or half-hearted and in times you JUST want to read SOMETHING/ANYTHING (Think of I want to eat something because I want to chew something and I have nothing else to occupy my time). In here you will not find original themes (except rarely). There is much repetition but usually with minor original details here and there. Not that there is not repetition of themes on the above percentiles BUT there, there are original twists and/or are good enough written that even the repeated themes will not mind you (if you take notice of them). Here you will find more grammar and spelling errors and/or even weird writing formats but as always there are exceptions and I forgot to mention it above but this also depends on whether the writer has a beta or how much English he knows.

~75%{+-15%} Crap to maybe readable ones. Really lame plots to passable but even if they are passable ones, there is so much bad grammar and spelling that the text is rendered unreadable... figuratively and realistically. This is the bulk of fanfiction unfortunately. Here you will find gray-cell-killers born from boredom, disgust, anger e.t.c.

So something like this. The above is mostly applied to English-written fanfiction since it is the only language except of my own that I can read. And also I must note that as always there will be exceptions in each percentile. For instance I HAVE found an excellent story but with grammar and spelling errors because the writer had no beta (thankfully not so much that I had to abandon it because I couldn't bare to read it - it was a good plot) and of course there are flawless writings in regard to spelling and grammar but with no plot whatsoever...

This is my take based on personal experience and three websites and it's a rough estimate that may not reflect opinions of others.