In this work we have shown how the neutron halo structure of nuclei affects reaction mechanisms. Our experimental study was applied to a single-neutron halo nucleus (11Be) and a two-neutron halo nucleus (6He) in their interactions with a lead nucleus target. The experimental setup allowed simultaneous measurement of core and halo neutron momenta, as well as target-nucleus excitation energy kinematical properties of the halo neutrons were collected from the new TOURNESOL detector, a liquid scintillator time-of-flight detector of large volume. Characteristics of this detector are well covered in this document. For the two beams, we obtained exclusive measurements in momentum width, distinguishing between break-up, stripping, and core fragmentation, as well as as several target-nuclei excitation energy ranges. With 11Be projectile, momentum widths for core nuclei and halo neutrons are in agreement for break-up reactions, and the target nuclei remain on excited. The measured values are about 10 to 15% larger than those given by similar studies done with a core-nucleus collected close to zero degree. Neutron momentum distributions after reactions involving a break-up of the 10Be core were compared to similar data with a 10Be beam. With 6He projectile, we studied correlations between neutrons and core momenta to conclude that break-up reactions exhibit a one-step process and that stripping reactions could occur in both one- or two-step processes. In this later case, the "di-neutron" structure of 6He ground state is responsible for one-step dissociation process, while "cigar" structure in most likely responsible for the two-step dissociation process.