Suppose that I have an HPLC with a variable wavelength UV detector, as well as two pure protein samples that differ by a point mutation (otherwise same concentration, extinction coefficient, buffer conditions, etc.). If I run them through the same column sequentially and integrate the A280 peaks after baseline subtraction, should I expect the areas under the curves to be the same? I guess another way to ask the question is whether the absorbance unit is something that can be compared from run to run, or is the elution volume/peak shape the only physically meaningful quantity for comparison?
There is nothing absolute in HPLC related measurements. Take the easiest example first. Think of a separation of a racemate using a chiral column on a UV detector. After injection, you will see two peaks, with different retention times, and equal peak areas. Their absorbance at the peak maximum will be different because both peaks will have different widths. Change the flow rate and now your peak areas change but their peak ratio will still be 50:50.
The same ideas apply in your case. You state that everything is same (conc., molar extinction coefficient etc.). In HPLC, your peak areas will be affected by flow rates only given the rest of the conditions remain identical.