We present a combined study by quasielastic neutron scattering (QENS), dielectric and mechanical spectroscopy, calorimetry and wide-angle X-ray diffraction on single-chain nano-particles (SCNPs), using the corresponding linear precursor chains as reference, to elucidate the impact of internal bonds involving bulky cross-links on the properties of polymer melts. Internal cross-links do not appreciably alter local properties and fast dynamics. This is the case of the average inter-molecular distances, the β-relaxation and the extent of the atomic displacements at timescales faster than some picoseconds. Contrarily, the α-relaxation is slowed down with respect to the linear precursor, as detected by DSC, dielectric spectroscopy and QENS. QENS has also resolved broader response functions and stronger deviations from Gaussian behavior in the SCNPs melt, hinting at additional heterogeneities. The rheological properties are also clearly affected by internal cross-links. We discuss these results together with those previously reported on the deuterated counterpart samples and on SCNPs obtained through a different synthesis route to discern the effect of the nature of the cross-links on the modification of the diverse properties of the melts.