This table compares some relevant numbers for the two aircraft:
||575 000 kg
||447 700 kg
||4x 348 kN
||4x 296 kN
|Thrust / Weight
(All values from Wikipedia (A380, 747-8), all at MTOW, standard sea level conditions)
As you can see, the 747-8 has a slightly higher thrust to weight ratio (about 9% higher), which means it can accelerate a bit faster (at MTOW). However, the A380's wing is much larger resulting in a smaller wing loading (about 14% lower) at MTOW. This results in a lower takeoff speed and therefore reduces the required runway for takeoff.
If you want to compare the takeoff distances at different takeoff weights, I recommend to look at the Airport Planning Documents. These will contain graphs like these:
(Airbus Aircraft Characteristics document for the A380, ISA conditions, Trent 900 engines)
(Boeing Airplane Characteristics for Airport Planning document for the 747-8)
The second graph shows that at MTOW the 747-8 requires a little over 3000 m of runway for takeoff (at sea level). At the same weight (about 448 t), the A380 only requires about 1750 m according to the first chart. This is because it has a much lower wing loading of only 530 kg/m² now. With a 3000 m runway, the A380 can lift off at over 570 t, more than 100 t heavier than the 747-8.