I would like to know if there are any limitations of frameworks such as Petri nets (with its extensions) or pi-calculus that bigraphs developed by Robin Milner do not have.
If there are none, then what is the advantage of using the latter over Petri nets or pi-calculus?
There is not one right model of computation that works at all levels of abstraction.
You already see this when you compare $\pi$-calculus with Petri-nets: $\pi$ is based on binary interation, while Petri-nets can synchronise $n$ parties atomically for all $n$. It is known that general $n$-ary synchronisation cannot be reduced (simplifying a bit) in a compositional way to binary. synchronisation
I think Milner developed bigraphs, in part in reaction to spatial calculi like the Ambient Calculus, and Nomadic Pict. Spatially located computation can also not be reduced (simplifying a bit) in a compositional way to $\pi$-calculus-like interaction. Bigraphs are a natural and flexible approach to modelling (changing and unchanging) linking structure, including location. The hope has been that a lot of the technology developed for process calculi lifts naturally to those more general setting.
