Electron affinities of the chalcogens and halogens
The amount of screening is the same in the two groups but the effective positive charge that the incoming electron feels is stronger in Group 7.

For instance, oxygen has the electronic structure of 
$$\ce{1s^{2} 2s^{2} 2p_{x}^{2} 2p_{y}^{1} 2p_{z}^{1}}$$ and 8 protons. The effective positive charge that pulls the incoming electron (which approaches the second level) is $8 - 2 = 6$. 

In fluorine we have,
$$\ce{1s^{2} 2s^{2} 2p_{x}^{2} 2p_{y}^{2} 2p_{z}^{1}}$$ and 9 protons. The effective positive charge is $9 - 2 = 7$.

Therefore, the net pull from Group 7 is stronger than Group 6.