With regard to the following:
the mean of a Binomial dist is n*p$np$
the variance is np(1-p)$np(1-p)$
the mean of a Poisson dist is lambda$\lambda$, which we can imagine as n*p$n\times p$
the variance of a Poisson is the same as the mean
Now, if a Poisson is the limit to a Binomial with parameters n$n$ and p$p$, such that n$n$ increases to infinity and p$p$ decreases to zero while their product remains constant, then assuming that n$n$ and p$p$ are not converged to their respective limits, the expression np is always greater than np*(1-p)$np$ is always greater than $np(1-p)$, therefore the variance of Binomial is less than that of Poisson. That would imply that Binomthe Binomial is below in the tails and above elsewhere.
