Others have responded, so I'll say this: I've booked the most likely route for a 777-300 three times and three times the plane has been swapped (often the night before). It seems super-hard to secure definitively. However, I'd also add that one of my best F experiences was on the 777-200, thanks to an amazing crew.

If you want a good compromise, I'd always recommend the 787-9 or 787-10. You get a fairly modern F (2015) on a quiet plane. I flew F on the 787-10 to IAH in June and the cabin still looked relatively new (compared to the ancient grubby A380's F seats with a ridiculous IFE which just doesn't work - and yet we pay F rates for this seat and some people here prefer it! Perplexing...).

However, like others have said, I wouldn't try and pick routes based on you *might* get a 777-300. The plane can often get swapped out!