Given your height and desire to sleep, I'd say definitely pick the 3-class 777. Some of the 2-class planes, the 767-300ER in particular, have a different seat design that has less length and less space for your feet to rest when sleeping. I find even the bulkhead of these planes, while having a very large footwell cutout unlike the rest of the plane, still have short length. The middle seat in these aircraft sounds great in practice, but they are extremely compromised as far as length is concerned. I'm 6'2" and I simply cannot lie flat or sleep in these seats. Further, I've had my drink spilled twice due to the tight aisles.

The 3-class 777 will have a denser cabin, but the seats are noticeably longer and IMO have slightly better cushions for sleeping. Both planes will allow you to collapse the armrests for more width, but the 777 seat is a smidgen less wide (I don't think it's 3" though).

One last thing - since the 777 is a 3-class plane, you can pay for an upgrade into F (or on the oft chance possibly be operationally upgraded), and that seat is the pinnacle for sleeping (they provide a mattress pad).