Take off performance is regulated by the requirement for an aircraft to achieve a minimum climb gradient with one engine inoperative. This means that a twin engine aircraft (B777, A330 etc) will, under normal circumstances, be climbing with approximately double the minimum power required (and airlines will often use the minimum power required in order to preserve engine life - which reduces costs). However, the 4-engine aircraft will only have 33.33% more power than needed for the emergency case.
Hence normally the 2-engine aircraft will often appear to have better climb performance than their 4-engine counterparts. This is the case at high take-off weights; a 4-engine aircraft with no passengers/freight and a small fuel load (eg on a positioning sector) will most likely climb like a homesick angel!
As with most things in aviation, the details are much more complicated, but this is a broad generalisation.