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DOF can change, its lens dependant, not F-stop dependant. It shouldnt be too much, but in real life some F2 lens have DOF like F1.4 and some like F3.5. Might be tied to number of elements, but it might be also tied to fact that official focal length isnt always real focal length. (eg. lens can have 186mm and advertised as 200mm, or should be 25mm but in real life its more like 27mm).
I think that especially at wide-angle settings, zoom can be bit inaccurate as far as focal length settings go.
Canon 24-70mm f2.8
Transmission part - its pretty consistent, so it probably really is f2.8 with it appropriate light gathering capability, but it doesnt say how much DOF it has. Metrics for 35mm f2 are unfortunately unavailable, so no clue if it transmits more or less at f2.8.
Nikkor 24-70mm f2.8
Gives clue, that not all lens are made same, maybe Canon 24-70mm f2.8 isnt "that much f2.8" .. which could explain less DOF.
Bit too many variables here..