The 787 has a significantly longer range than the 767/330. That fact alone a very large impact:
1/ It is much heavier than those, and costs a lot more in fuel on takeoff and landing, which makes it a bad choice for the short-but-heavy-load routes that the 767 and 330 excel at (HKG-TPE, CTS-HND, etc). So it's a bad replacement and competitor in those markets.
2/ On the other hand, it opens up ultra-long-range point-to-point flights that weren't quite possible before without a jumbo (e.g. UA on SFO-SIN, or routes to secondary Chinese cities like XIY, CTU, CAN, etc.)
1/ It is much heavier than those, and costs a lot more in fuel on takeoff and landing, which makes it a bad choice for the short-but-heavy-load routes that the 767 and 330 excel at (HKG-TPE, CTS-HND, etc). So it's a bad replacement and competitor in those markets.
2/ On the other hand, it opens up ultra-long-range point-to-point flights that weren't quite possible before without a jumbo (e.g. UA on SFO-SIN, or routes to secondary Chinese cities like XIY, CTU, CAN, etc.)