So it's definitely rare. Personally I love 777s--part of the attraction is the monster turbofans. Most long-range models have GE90 engines, which are total beasts. They incidentally have extremely low shutdown rates.
The 777 is my favorite also, it's a beautiful well-designed and well-built plane with an almost unbelievable safety record. (Barring being sabotaged by the pilot, or being shot down by a surface-to-air missile, which are hardly things you can blame on the aircraft itself.)
Still have not flown in a 787 as I mostly fly United and they don't have too many of them in the fleet yet. Ironically it's mostly 747s on the routes I regularly fly to Europe so I get to experience them regularly along with the odd A-380. (The latter a comfortable ride but just no poetry in the thing. It looks like a squashed frog.)
Note that Rolls Royce faces stiff competition with chiefly General Electric as the engine supplier for the 777 line.