Problem is there's lots of variability on the day due to payload and/or derate but in general as pax has said you'd expect the big twins to climb steeper than the 4 engined types. Can't speak for the 380 but for the 747,777, and 787 the basic take-off technique is to typically rotate towards a target pitch attitude (13-15 degrees typically for a 777 or 787, can't remember the 747), then holding a fixed speed climb to (usually) 1000 feet and only then flattening the climb and accelerating to en-route climb out speed. Whether the 380 has a more sophisticated technique I do not know, but don't forget(?) there is not just noise to think about, there are also other "little" issues like mandatory minimum climb gradients and obstacle clearance to be considered, so I'm not sure too much scope for finessing of the climb just after liftoff.
I suspect the difference in noise level you are perceiving is almost all down to engine design, the 747 suffers from being relatively long in the tooth in that department.