Now if I'm wrong about ID, and that it does in fact attack the Darwinian theory of evolution and natural selection, then I guess I'd need to know more about their claims.
The reason that ID in its current form is incompatible with scientific explanations of biodiversity is that its main "legitimate" proponents, William Dembski and Michael Behe, build their cases on the assumption that there is a hard and-fast dichotomy between design and chance plus selection. They assume that no necessisity can exist for structures more elaborate than a certain (not ever defined) level of complexity. It follows then, that these things can not have resulted from selection pressures (i.e. evolution) so they must have been designed from a pre-existing plan. This "plan" implies the existence of an intelligence actively at work in creating new life forms.
This is a rehashed version of the "God of the Gaps", where automatically, we conclude that anything that current scientific knowledge can't explain is the work of God, or, in other words,
magic.
Clearly, this is not suitable for scientific testing.
The claim that God exists, and set in motion the Big Bang, complete with the physical laws that circumscribe all possible events in the natural universe is different for a couple of reasons.
First, everything that is currently accepted in the physical sciences points to the conclusion that scientific reasoning does not,
can not apply to pre-Big Bang conditions.
With the exception of some versions of the Anthropic Principle, science has tended to accept the values of the fundamental physical constants as "givens" without worrying too much about why they have the values they do.
Science, while basically sceptical in approach, does accept some things as axiomatic. "Energy can neither be created nor destroyed", E =MxCxC, F=ma, etc.
So, whether these laws came from God or just
are, is irrelevant to scientific investigation. The only characteristic of God that a theistic scientist has to accept is that She doesn't micro-manage the natural world.
Atheist scientists know this to be true, because there is no God, so both types of scientist can get on with science, using the same set of assumptions about the natural world, and leave theology to others.