Some clients with heavy web traffic are impressed by the amount of data processed and the speed at which the reports are updated - typically within 2-3 hours. For non-Premium users the wait was often 24 hours or more.
Google Analytics has terrific visitor segmentation capabilities, but Google Analytics Premium really makes that useful for Enterprises because data sampling is eliminated. This allows marketers and analysts to construct very specific user segments and see 100% statistically valid trends and datasets.
I believe the Attribution Modeling reports in Google Analytics Premium are among the best in the industry. GAP provides seven pre-defined models (first click, last click, time decay, etc.) but more impressive is the ability to create custom models to your liking. This allows marketing executives to truly analyze lift and performance across channels without worrying about duplication problems, and provides the data necessary to allocate marketing budgets for maximum profit.
I would highly recommend Google Analytics Premium to large organizations or enterprises that already use Google Analytics or a similar solution. The advantages to GA Premium are threefold: 1) More data collection, 2) Advanced features for custom analysis, and 3) Enterprise service and support.
There are several main reasons to switch, and depending on your needs you may find one of these more compelling than others. Our clients typically switch to access additional custom variables or to gain the ability to download unsampled reports. Other clients have switched due to data limits (ex. sending more data to Google Analytics than the standard ToS allows for).