Which heart rate zones did you set on both devices? are they similar or different. They can be different if one is used and adjusted to running and the other to heart rate zones of cycling.
In Garmin Express/Connect you can define two different sets of heart rate zones and VO2max for both running and cycling. Please check there.
Even if all zones are all identical then still there is a chance that the forerunner and the Edge give different values
If the forerunner is fully set up for running (by Garmin) and the edge1030 specifically for cycling they can give different training loads for the same exercise. This is because the formula used to calculate the Training Load is more or less 'hard programmed' in the device, unfortunately, and cannot be changed/adapted by the user.
