  We discuss the energy and angular distributions of two emitted neutrons from
the dipole excitation of typical weakly-bound Borromean nuclei, $^{11}$Li and
$^6$He. To this end, we use a three-body model with a density dependent contact
interaction between the valence neutrons. Our calculation indicates that the
energy distributions for the valence neutrons are considerably different
between the two nuclei, although they show similar strong dineutron
correlations in the ground state to each other. This different behaviour of the
energy distribution primarily reflects the interaction between the neutron and
the core nucleus, rather than the interaction between the valence neutrons.
That is, the difference can be attributed to the presence of s-wave virtual
state in the neutron-core system in $^{11}$Li, which is absent in $^6$He. It is
pointed out that the angular distribution for $^{11}$Li in the low energy
region shows a clear manifestation of the strong dineutron correlation, whereas
the angular distribution for $^{6}$He exhibits a strong anticorrelation effect.
