I find them funny above all.
It's sweet to see that someone is so proud of his/her family, but just like we're our own worst critics, I think the Christmas letter turns us into our own biggest horn-tooters.
I've read dozens of these every year, mostly from people like my mom's college friends we've seen twice in the last 30 years. Aside from the rare truly entertaining narrative, I question why people would think near-strangers would want to know whether Bobby got A's and B's or B's and C's, exactly which softball tournament Jenny got her first home run in and the date, etc. People who want this level of detail are probably in regular contact with you anyway. Keep it simple and less than 2 double-spaced (1 single-spaced) page!
It's good to include a photo, with names and ages on the back. Mom also gets a half-dozen a year where she has to guess who's who!
To your last point, I don't know if they're outdated or if we just see fewer of them now that my mom's friends are grandparents or parents of young adults, and my friends are single or have kids under 5 (pics please, but "accomplishment" stories ring kind of hollow beyond basic, adorable milestones). I would guess that things like Facebook make them less common.