Who allows fewer runs: a pitching staff that strikes out a lot or one that doesn't?

Chicago Cubs pitchers have led the National League in strikeouts for the last seven consecutive years. But they've never led the league in ERA during that strech. Striking out batters suggests more dominance on the part of pitchers, but it also leads to higher pitch counts because a strikeout simply requires more pitches. Also, strikeout pitchers are more prone to control problems.

Is it a good thing for a pitching staff to strike out a lot of batters?

Here is some evidence that suggests yes, it is a good thing.

Based on the 2007 season, pitching staffs that strike out more batters collectively have better ERAs: