Our customers (>50% of whom are using Gmail) claim that our accuracy is significantly better than that of Priority Inbox - and without any training required.
This is because our algorithms study the relationship trees in your email history (without ever looking at the content of your emails - for security and privacy reasons) to decide which emails are important to you personally. Priority Inbox, on the other hand, seems to apply a global set of rules which are not personalized to you. We also have lots of other features in addition to filtering, and are constantly building more.
To let numbers speak for themselves, if you're getting at least 60 emails per day, there's a 52% chance you'll convert to a paying customer after the free trial (and we don't ask for a credit card upfront). In other words, we're not exactly sure why we do a better job, but our customers tend to think it's worth paying us money for.