It depends on what rind of markers you use. If you measure oxidant/antioxidant activity you will find great difference between plasma and blood/ See: Electroanalysis, 2009, 21, No.3-5, 618-624
One of your major antioxidants is glutathione and it is mostly found inside your red blood cells. This is also true for the enzyme SOD. Therefore, when you look at only serum or plasma you do not get a good picture of the protection given to whole blood.
A sensitive measurement of total body antioxidant level would be reflected inside of the cell. In my opinion, if you were to get a more meaningful measurement of glutathione, it would be looking at lymphocytic glutathione levels, GSH/GSSG.