This table compares some relevant numbers for the two aircraft:
Aircraft |
Airbus A380 |
Boeing 747-8i |
MTOW |
575 000 kg |
447 700 kg |
Wing Area |
845 m² |
554 m² |
Wing Loading |
680 kg/m² |
808 kg/m² |
Thrust |
4x 348 kN |
4x 296 kN |
Thrust / Weight |
2.42 N/kg |
2.64 N/kg |
(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.