I would use the rubric to score the assignment if you want them to be the same. There's a checkbox you can hit that takes the rubric score for the assignment score.

That said, from my perspective, the LMG gives students holistic feedback on their performance on a criteria, which may or may not be the same as an assignment score. For example, to help students on the feedback, I gave completion credit (free points) for the assignment score. Then I would leave detailed rubric feedback on learning objectives that populate the LMG. Whenever I did conferences or asked students to check their progress, we looked at the LMG progress, not assignment scores. Our discussions focused on the material, not on gathering points.