Using atomistic quantum simulation based on a tight binding model, we have investigated the transport characteristics of graphene nanomesh-based devices and evaluated the possibilities of observing negative differential conductance. It is shown that by taking advantage of bandgap opening in the graphene nanomesh lattice, a strong negative differential conductance effect can be achieved at room temperature in pn junctions and n-doped structures. Remarkably, the effect is improved very significantly (with a peak-to-valley current ratio of a few hundred) and appears to be weakly sensitive to the transition length in graphene nanomesh pn hetero-junctions when inserting a pristine (gapless) graphene section in the transition region between n and p zones. The study therefore suggests new design strategies for graphene electronic devices which may offer strong advantages in terms of performance and processing over the devices studied previously.