One thing I have noticed is that Anonymous seems to be primarily comprised of a very small number of people who can actually hack — like, for real — and is otherwise mostly a mass of people who download script kiddie software and do what the actual hackers tell them to do with it.
I've seen the Pastebin pages and stuff where one of the real hackers explains what he wants all the followers to do, which software he wants them to use, etc, and then they blindly do it. It's this that typically takes sites offline because when you've got a huge mass of people willing to DDoS whatever you tell them to it gives you quite some power.
The more in-depth hacking like actually breaking into servers and stuff is most probably a much more connected and organised group of individuals though, akin to LulzSec but without the fancy moniker.
I don't have a great deal of respect for Anonymous as a whole because because they seem to have two main approaches:
[*:1idlqr3j]Hacking into sites with no real pattern or consistency, with targets ranging from the games industry to banks — this seems more like they're simply trawling security groups for new vulnerabilities in software and then exploiting them
[*:1idlqr3j]Throwing millions of machines and botnets at websites to take them offline
Neither of these things are particularly sophisticated or likely to have any kind of long-term effect on anything, which is why the many skilled hackers out there don't bother with this shit because all it does is get headlines and attracts attention. Most hackers do this kind of thing quietly and get rich. I suspect the few instances where Anonymous has actually done something worthwhile like exposing SOPA information has been the work of just one or two really good hackers who used the Anonymous name to get it out there.