The Army by a large margin. At the peak of the war the Marines had one division in country, the Army had the 1st Infantry Division, the 1st Cavalry Division, the 4th Infantry Division, the 9th Infantry Division, the 25th Infantry Division, the 101st Airborne Division, and the Americal Division, plus the 11th Armored Cavalry Regiment and a brigade of the 82nd Airborne Division. Now, a Marine division is somewhat larger because it includes an air wing while the Army gets air support from the Air Force. The Marines concentrated in the northern part of the country (I Corps), while the Army reinforced them and had the rest of the country (in American terms - the South Vietnamese Army was throughout, of course).
Edit. As some have pointed out, there were two Marine divisions for a time. Doesn't change the answer but does change the proportions. Sorry for the error.
Source: John Scales (Quora)
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