For me, I do think 2003-2004 (the Ghetto Nick/Nick & Paris era) was one of the darkest eras in their history. I'm focusing on Nick here because I really wasn't a Nick fan until Now or Never came out in 2002, and then it was hard to watch him sort of spiral downward over the next few years. From a group standpoint, though, that was also during their big hiatus between Black & Blue and Never Gone, when we didn't know if they were ever going to come back or not. There wasn't much going on with the group until AJ did that Oprah interview where the guys all surprised him. It was a good era for fanfic, but not a good time for actually being a fan of the group.
2006 was also a rough year... That was when Kevin left, and looking back, we now know things were pretty rough for Nick then too. But we did have Brian's solo album and tour that year, so that was the bright spot of 2006!
I have two favorite eras. One is the Millennium era in 1999 because that is when I went from being a fan to an obsessive teenybopper FAN and discovered fanfic and all that good stuff. I loved how popular they were then; they did tons of TV appearances and won awards and had videos on TRL, and it was so much fun to be a fan!
My other favorite era is the IAWLT era in 2013 because Kevin was back, and for the first time since he left, it felt like everything was as it should be in BSB land again. I loved how excited we all were about the new album, and I think that tour is my favorite one.
As far as fanfic goes, I like reading stories set in the good old days of the late '90s, before they all had their own families. I think it's easier to show their brotherly relationship in those old-school stories. I also enjoy present-day stories that put them in situations where they're together without the wives and kids being around. Erika and Mare are both good at doing that. I don't know that I necessarily have a favorite era to write in, as I usually write in the present or recent past.