It's hard to say definitively. The Hurricane was available in greater numbers. In August 1940 32 squadrons were flying Hurricanes vs 19 squads flying Spitfires. And this ratio more or less didn't change during the Battle. So the Hurricane had the advantage of numbers.

All told Hurricanes shot down more planes in 1940 than every other category combined (ground based anti-aircraft, French fighters, Spitfires, everything). Again the Hurricane had the advantage of numbers.

But it was an inferior fighter to the Spitfire. The Spitfire was faster, flew higher, turned better, and had a longer range. The Spitfire matched up to the BF-109s much better. The Hurricane did have another advantage (besides numbers), it was a more stable gun platform. Spitfires were much more lively. They tended to dance around making it hard for the pilot to draw and keep a bead. That desire for the plane to turn, made it ideal as a dog fighter. It also made it less ideal against bombers, which sometimes required several steady bursts to take down. The Hurricane was also a less sensitive machine (in 1940). Spitfires needed more maintenance. So those 19 Spitfire squads each flew less sorties than their Hurricane counterparts.

So the British used the characteristics of both planes to their advantage. Ideally an interception would go like this. The Spitfires would scramble first, the Hurricanes following close after. With their extra speed the Spitfires would hit the German formation and the German escort would peel off to deal with the attackers. Then the Hurricanes would arrive and deal with the bombers. Each plane was supposed to be used in its best role. In reality the ideal wasn't often perfectly met.

Both planes were being manufactured at high rates and both were critical to the fight. Both continued to be made until the end of the war. On the whole I'd credit the Hurricane as being "more important" in the BoB. Hurricanes flew more sorties and shot down more Germans. But without the Spitfires taking on BF-109s, the Hurricanes would have lost a lot of efficacy. So they can't really be taken in a vacuum.

Most of the data I pulled from World War II Combat Aircraft by Angelicci, Matricardi, and Pinto.