I think it's a bit deceptive that a person works hard for months to get to the 10K tools, to have access to the moderator tools, to find out that all it is is analytical tools. While they are nice, I think it would be best if an appropriate name could be found for these tools, perhaps advanced statistics, or something like that.
What do you think a moderator does? They moderate. They keep track of things happening on the site and step in when they notice (or are notified of) things going awry. Of course they're going to need a set of analytical tools to get the bigger picture of what's going on.
If you didn't think that was what most of the 10k/pseudo-mod tools were all about, then I think you deceived yourself. Honestly, I don't really see any reason to change the name, especially since the privileges page explains everything in detail.
Matt Haughey of MetaFilter recently released a video that describes all of the tools that they created over the years to help moderate their site with only 3 or 4 moderators.
Many of the tools are very similar to the ones you see as a 10k user. Matt Haughey's MetaFilter Video actually does a really good job of describing how all of the 10k moderator tools could be used to help detect problem areas and respond to them quickly.
While these may look like simple analytical tools, if you take the time to learn how to use them, you'll find them to be quite powerful.
But they are 10K moderator tools. You were expecting to open a world of ultimate power and slash & burn abilities; so in that sense, the 10K tools are a bit of a disappointment.
But, if you've been an active participant in the community self-moderation up to this point, the "10K moderator tools" are a panacea of information. They make it a lot easier to find activities that NEEDS community attention. The 10K tools are really important help the high-rep community see where intervention might be needed: where edit wars are going on, where new tags with typos have been made, which questions are spam, etc.
10K moderators are the sentries of the site; They provide the lookout. They have a lot more oversight about what is going around key events in the site: extreme voting situations, decisive voting activities, new user posts, new tags, etc. But for the really "heavy lifting", where direct intervention is needed, users can flag the diamond ♦ moderators.
Check out Matt Haughey's Video Offering Advice to Community Moderators. This information will help you understand how these types of tools can help in everyday community moderation.
But besides all the reports and back-room insights, there are a few new active powers that 10K moderators gain. Most notably, 10K moderators can finally DELETE closed posts which the community decided no longer belong on the site. +10K users can so also see deleted posts. They can also undo much of this activity, if something goes wrong. 10K moderators provide a bit of checks-and-balances where the community and other moderators do something unexpected.
The whole idea is to get in the habit or lending a hand with the routine cleanup work. Check the latest closed posts to decide what no longer belongs on the site (off topic, spam, etc).
These community moderator activities keep the site sleek and high quality.
Congratulations on your new reputation abilities!
For anyone who is not familiar with the 10K tools feature, here is a quick overview of what is to come:
Users with +10,000 reputation become what is known as a "10K moderator." It is the highest level of "community self-moderation" just short of the voted "diamond ♦ moderators" which are voted on by the community.
In the top bar where you have the 'Chat', 'Main', and 'FAQ' options, there will be another menu option called "Tools".
The menus and help text list the basic tools available there:
The key power that comes with the 10k dashboard is the overview of what is going on with the site: seeing what posts are getting flagged, what questions are getting close and delete votes. This overview marks a very important divisions between those who are working with this and that question thread and those who have the power to participate in the management of the site.
It makes perfect sense to me to call that the division between regular users and moderators, notwithstanding the existence of degrees of trust within the body of the users who have this administrative overview.
Still, access to moderator tools doesn't make you a moderator, so maybe we are better off with something like status tools.