What do you like best?
Omniture/Adobe Analytics is incredibly flexible. I can create custom variables for all our various report suites, and then build dashboards for internal (and in rare cases, external) stakeholders.
While the UI takes some getting used to, it is at least internally consistent--the submenus nested within OTHER submenus might not be how I'd design something, but the organization logic makes sense so that a new user can adjust and find new things on his/her own.
It's also relatively easy to pull data offline for analysis via export, and can be done over large time ranges as well as with thousands of rows (though in the latter case, you have to hack up the URL in order to get that much data at once; the UI itself doesn't support it.)
What do you dislike?
The documentation for Omniture is frequently stale, and the support is offshored and frequently doesn't understand its own product.
In one case, when trying to change page tags, documentation asked us to use a "tag manager" product in Adobe. Upon asking support about this, they tried to sell us a consultant to help with the implementation. Upon further digging, it was revealed *by support* that the product no longer existed, meaning they'd attempted to sell us consultant time for phantomware.
Most interactions with support are like this--they're well-intentioned, I'm sure, but don't undrestand the product or keep up with its updates.
Recommendations to others considering the product
If you're doing e-marketing, then you might consider Adobe Analytics, as it's rolled into the entire Adobe Marketing Suite--where most of the other offerings are geared toward ecommerce.
If you're just doing this for publishing or basic website measurement, though, you'll be paying for far more than you want/need.
What business problems are you solving with the product? What benefits have you realized?
This is for digital publishing, so for the most part the questions boil down to "what content is most read, by whom, and why?"
This informs editorial decisions. We also have some level of tracking that looks at "where are people clicking, and why" which helps with site design in order to increase user retention.
In general, we are better able to position our content both off-site (think SEO, social media) and on-site (think recirculation modules) because of the data we get out of this platform.