The founding of the OKH (Oberkommando des Heeres) took place in 1935. it was part of one of the last revisions of the Versailles treaty, as Germany took full controll over it's military again. The OKH coexisted with the surpreme commands of the air force and the navy.

The OKH was subordinated to the defence ministry (Reichswehrministerium) which was a remnant of the Weimar Republic.

In 1938 Hitler got rid of high-rank military officials which critized the aggressiveness of his foreign policy. He uses this incident to take more control over the Wehrmacht by founding the OKW to oppose the OKHs power.

This polycracy (reign of many) is something which was very distinct in nazi Germany. The rivalry of many concurrent political organisations like the bipolarity of the hierarchy in the NSDAP and in the State itself or the OKH and OKW was manipulated by Hitler to gain as much power as possible and make everybody dependent of his will.

Initially in WW2 the OKH was de facto more powerful, as it controlled the main theatres of war. The OKW couldn't influence it without Hitler's direct command.

In late 1941, after the defeat at Moscow and failed Blitzkrieg in the CCCP, the OKW began to gain superiority over the OKH and Hitler took more and more direct controll over how the war was fought. The chief of the OKW Wilhelm Keitel never opposed him.

TLDR; The competition beetween them was intended. Hitler could keep much influence over the warfare by manipulating the two organisations. Until 1942 the OKH was more important, then the OKW took over.