Oversimplified, of course, but I suggest these are useful frameworks for comparing the two modes of thought.
Intelligent Design first:
(1) Postulate: There is or was a designer.
(2) Observation: The universe and the life within it are of complex design, but there are commonalities within them.
(3) Contention: Pure chance is unlikely to have resulted in such complexity and commonalities.
(4) Implication: A designer must be responsible for both the complexity and the commonalities.
(5) Conclusion: There is or was a designer.
Technically, a postulate is something offered without proof. It is a given. The IDists offer complexity as evidence for a designer, but it is clear they have presupposed there is or was such a thing. So, in effect they are guilty of circular reasoning.
(1) Observation: Living creatures are diverse and complex in form, but share commonalities.
(2) Hypothesis 1: External conditions exert pressures on populations of living creatures, forcing them to adapt to survive or ultimately to die off.
(3) Hypothesis 2: Given long enough time, these external conditions resulted in the organisms we see today.
(4) Evidence 1: Living creatures share common biochemistry and similar genetic material.
(5) Evidence 2: Diverse external conditions resulted in diverse adaptations.
(6) Evidence 2: The fossil record indicates many living creatures existed in the past, but no longer. Similarities exist between these former organisms and present-day ones.
(7) Evidence 3: The time available for such development was at least 3 billion years.
(8) Conclusion 1: The commonalities among living creatures result from (4).
(9) Conclusion 2: The diversity among living creatures results from (5).
(10) Conclusion 3: (6) and (7) support the hypothesis that external pressures have shaped the development of living organisms.
Science is observation, hypothesis, evidence, conclusion. The evidence either supports or refutes the hypothesis. Darwin, the principal developer of the theory of evolution, followed exactly that pattern. He did not presuppose a single, unverifiable reason for the diversity and complexity of living creatures, but in fact assumed (with good reason) that were many reasons.
Evolution, taken to its ultimate conclusion, implies that at one point in the dim past there was a common ancestor for all of earth’s creatures. There is of course debate about what transpired to create that first common ancestor. Evolution, if it is to be self-consistent, must presume that chance resulted in the first common ancestor. The possibility seems to be hopelessly remote, but it only had to happen once.
ID removes chance from the equation entirely in favor of a single ultimate Cause, for which there exists no independent evidence. From a faith-based perspective, this argument is sufficient, since faith in essence supplies the missing evidence. The fact that the universe and the life within it are complex does not prove there is or was a designer or an ultimate Cause. It just proves that the universe and the life within it are complex.