Rather than explaining what Mozilla scores over Chrome, it would be better to compare them under separate headings. I am making an attempt at such a comparison.
1. Performance and Memory
Memory-wise Chrome takes much memory than Mozilla. In fact, Mozilla is 7% more efficient than Chrome with 10 tabs opened in both. Though the difference is little, it becomes important with more tabs open. Users preferring efficient memory usage will opt for Mozilla. But Mozilla takes longer to release memory once the tab is closed.
Chrome has been observed to be more stable. It employs a technology where each tab runs as a single process independent of other tabs.
3. User Interface
Mozilla wins in this section. It has customizable layout. Mozilla also allows windowed browsing, while Chrome lacks it.
Chrome provides a number of security features. Though, Mozilla has recently been adding a few security add-ons.
There have been several concerns about Google indulging in user data collection to enable it to target marketing. Since Google earns through user tracking and advertising, it misses some of the features from Mozilla. Mozilla, on the other hand has an effective control of cookies.