Don't have any manuals to hand today so I'll have to generalise.
The main difference comes down to the initial climb performance.
For the two-motor-machine, one loses around 50 percent thrust with a modest increase in drag ... resulting in something in the region of 80-90 percent climb gradient performance loss comparing AEO > OEI.
As a consequence the AEO takeoff case is very sporty and the raw AEO distance (at, say, 10-15 percent gradient) generally is considerably less than the OEI (at around 1.6 percent). Even with the 15 percent penalty, AEO TODR tends to be less than OEI.
For the four-motor-machine, one loses only 25 percent of thrust, again with a modest drag increase. The magnitude of the delta between AEO and OEI is very much smaller. With the 15 percent penalty AEO often comes out the loser and AEO TODR is limiting.
As with all such stories, generalisations only go so far and one should cite a specific AFM to come up with quantitative data.
... and, with the Eva Air shot, without any knowledge of the runway, it is not at all necessarily evident that the runway head is where one might presume it to be from the photograph .... ?
Nonetheless, it is a ripper picture ..