For the same wing span the induced drag of the biplane is a factor of the square root of 2 smaller than for the monoplane. The biplane has two disadvantages: you have to build an extra wing and it looks old fashioned. You should disregard the second and as for the first, you avoid building that thick pancake that will probably have to be mounted on folding struts to fit into the hangar on board. Of course, I came on the biplane to give the antenna a greater height, much greater than with that pancake.
The British had an AWACS type project with the Comet airframe and antennae for and aft. It didn't look nice and it proved to be too expensive, just as the Comet derived Nimrod MR4's they are now destroying.
I think we have some mix-up in terms.
When I mentioned "given the same span and wing area " what I meant was for the bi-plane with a 2 identical wing with individual span of X and Chord of Y, the total span for the aircraft would be 2X.
if one construct a mono-plane with wing of span 2X and kept roughly the same chord of Y. the wing area would be the same. but because aspect ratio this single wing is higher your tip loss is also smaller, thus you will have a higher L/D, given the mach and alpha. now given the same wing area, the bi-wing will give a smaller wing root bending moment which will save some structure weight.
now of course I am not counting on the bi-plane's wings to be close together and advantageously affect each other thus may obtain some good pressure gradients.
Israeli's Eitam has 2 L-Band electronically steered antenna mounted outside of the body skin on each side and 2 in fore and aft bulb. not same as the swinging array Nimrod AEW has.