The 380 relies on new engine versions, RR
Trent 900 and GP
7200, both rated at 70klbs, 77klbs for the somewhat heavier freighter version.
That's not enough for the 777 mainly since it has only one engine instead of three in case of engine failure during take-off.
The various versions of the 777 relies on engines from all three large engine manufacturers with some 85 to 115klbs thrust, the largest only from GE
If the rumors about a future stretched 380 (380-900) show to be more than rumors, then we will see it with engines approaching the same max thrust as the low end of 777 versions.