Complexity is usually measured as a function of the number of elements in a system and the number of relationships between those elements. By this measure, modern cells are more complex than primitive cells. The primitive prokaryotes, no nucleus and usually only a single DNA strand, are much simpler than the later eukaryotes with their cell nucleus and many chromosomes.
I understand that you would like to leave structure out of the equation, but I question whether that's really valid, and even if adhere to your preference of only considering reactions, the difference in the number of reactions and interrelationships between reactions for primitive versus modern cells is still dramatic.
While evolution doesn't have to increase complexity, in practice competition puts species into an evolutionary arms race, and this generates complexity as species are forced to perform continual evolutionary one-upmanship.
--Percy
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