I've been looking recently at animal count data that I've modeled
as Poisson with an observation level random effect, and have
worried a bit about such issues.
The observation level random effects model and the over-dispersion
model add variances on different scales -- for the observation level
random effects random effects model the added variance is
proportional to the square of the Poisson mean, whereas for the
over-dispersion model it is proportional to the mean. (These
comments assume small additional error; but they do delineate
the broad ballparks in which the two models operate. The glmer()
function is making its own very specific assumptions about the
scale on which to add the additional normal error.
The models are thus pretty much equivalent only if the range of
expected values is small. It would be useful to have more flexibility,
at the observation level at least, in the modelling of the extra-Poisson
error. Among the various packages that handle GLMMs, do any of
them offer such flexibility, maybe allowing e.g. a quasi-Poisson error?