Another difference is that the Drake equation is grounded in empirical observation - ie the parameters are based on the observed human position. So the equation is constrained to finding the probability of intelligent life like us.
However the ID version of the drake equation, which would be something like "the probability of an intelligent designer of life" has completely unknown parameters, as we know of no intelligent designers of sufficient ability to base the search on. We neither know the design method, or the motive.
Yet despite this it is ID which is claiming a definite conclusion. They don't simply say "our research is not conclusive yet". They are right out there saying "yep this flagellum *must* be intelligently designed". Wheras astronomers/cosmologists on the drake equation do not claim a definite conclusion even though they have a lot more background info about what intelligent life would be like.
I hope they find some intelligent life. We could use it here on Earth.