Is it more effective to run 30 seconds and walk 1 minute 10 times, or run 1 minute and walk 2 minutes 5 times?
This doesn't really meet the description of High Intensity Interval Training (which others have suggested) since it doesn't work different muscles or use full-body movements.
If that's your goal (or any metabolic effect) I'd suggest looking for proper HIIT workouts.
What you are asking about seems more like the Galloway Walk/Run method of distance running.
If, by "effective" you mean total distance covered and calories burned, I'd say the shorter interval sequence will be more effective.
The reason has to do with how your body recovers from short efforts.
Recovery times over a minute are only useful for sprints, and if you are doing sprints, you won't do full minutes of sprinting, unless you are already in great condition.
For practical purposes, you're goal is to almost completely recover during each walk.
You will then put best effort into the next Run.
Not coincidentally, this short of short intervals or what Galloway begins with.