That is very difficult to say. I made a thread (possibly might have been a reply to someone) a good long while ago on the math between choosing one or the other, and I found that executioners is always better against Mundo if Mundo is ulting (especially if he has spirit visage).
The key question on choosing executioners or giant slayer is mostly on their team comp and who is fed on their team. If they are a heavy sustain comp with things like soraka and Mundo, grab executioners.
If they are building lots of health but most of them don't have much sustain, grab a giant slayer.
If they aren't stacking health, and they aren't stacking sustain, but they are grabbing lots of resistances (unusual but still possible), grab an upgraded executioners because their adc is probably going to grab some lifesteal and this makes it easier to duel him.