If stabilizers weren't important people who can bench 225lbs would be doing 110lb DB presses.
Your example only shows that there's somewhat of a difference in the amounts lifted, nothing to do with difference in development using one or the other.
Same thing with machine weight vs. free weight, the amounts lifted vary, which doesn't really matter. Just add or subtract a little resistance and you have the equivalent. Doesn't have to be the same. And if going from machines to free weights the amounts lifted will initially be lower, then go up in a few workouts to around the same thing as the body aclimates.