The therapeutic index for ibuprofen is considerably better: it's around 10, fairly similar to alcohol. Accidental overdoses of ibuprofen are rare.
The main issue with ibuprofen is that it can have fairly annoying (but non-life-threatening) side effects like stomach upset and GI bleeds even with normal dosing.
It can also cause kidney damage which can be life threatening, especially when you’re dehydrated (which is pretty common after drinking); tylenol is a lot safer than ibuprofin when used as directed, it only becomes dangerous when glutathione is depleted (at which point it becomes a lot more dangerous, which is why you should never drink while taking Tylenol)