I find that fansubs add wanton profanity too much (they aren't dropping F-bombs in Naruto, a show marketed to 10 year olds) and there's a desire to turn every episode into a lesson on Japanese culture via translation notes. One exampled that always pops into my mind is when someone wrote a line, "This [japanese word for rice ball] is great." and then they added a translation note saying that the Japanese word meant rice ball. Wtf didn't they just translate it as rice ball the first time and get it over with rather than flood the screen with text? Plus a lot of them are kinda human garbage. The site for any group that does a moe show of any type is going to littered with words like "fag" "nigger" and jokes about child rape. Additionally, I don't see the point of them when the majority of anime gets simulcasted for free these days.
The general fansub experience is one I find to not be worth it. I find that Crunchyroll's subs are usually the best. They have a bit more personality than official subs but they don't go to gutter trash or translation note fiesta levels like fansubs do.
Usually I'd pick official subs, they're more professional and I'd hope more accurate. In Clannad and Clannad After Story's case though, fan subs all the way. The official sub for that show isn't anywhere near as good. One of the character's defining characteristics is that she refers to herself in third person, and in the official sub they completely ignored that and had her talk like everyone else.
So yeah, in some cases, the fan sub groups just care more about a series and it's fans, and because of that the subbing is better.