I happen to be one of the better placed people in the UK to comment on how much mobile networks know about you, as mobile customer analytics happens to be my profession, and I have worked with operators closely.
The answer is much more the former (anonomyzed user X...) than the latter, pretty much across all networks. Most of them outsource their ad serving to companies like Double Click or 4th Screen, Amobee or JumpTap, and will not share your data with them except as a hashed or doubly hashed number as a user ID. And that data is very, very limited...age range (not age), gender, maybe a lifestyle or interest classification for ad targeting, depending upon network. No personal details such as where you live, etc. That's not to say they don't know more, and couldn't learn more - but in terms of mobile ad targeting, that is pretty much the limit in the current environment.
As for mobile networks knowing more than the internet companies, that is hardly the case - mobile doesn't have cookies, and as such state-dependent knowledge is harder to acquire and maintain. Nor is there yet much ecommerce on mobile, which can be a huge factor in building a personal profile on the wired internet. Mobile may be better at linking their billing data to you for profiling, but over 50% of the UK mobile market is on prepay SIMs with no bills. All in all, customer profiling for mobile is still quite a challenge, and much harder than on the wired internet.
Not to say that mobile won't catch up...real-time traffic analysis and sophisticated contextual analysis of web browsing are on the horizon for mobile. But not this month...