If the tire starts to slide, you reached it's traction limit (by definition).
Also, you cannot apply the same braking force when applying only rear vs only front brake. If you apply only the front brake, and you keep gradually increasing intensity, you keep increasing front load as well, increasing the front tire's resistance to sliding. On a high traction surface like a road or sidewalk, I'd expect most bikes to be able to put 100% of their load on the front tire while braking (picking up the rear tire), which then allows your deceleration rate to only be limited by the bike's geometry and resistance to flipping over the front wheel. On the other hand, it's not physically possible for the rear to provide this much brake force, since as you increase deceleration, the rear end has less and less load. You'll always hit the tire's traction limit and therefore induce a slide at some point which is lower than the front limit.
Note that on a very slick surface, the opposite could be the case. If your grip level is low enough, the peak deceleration rate still won't cause very much load transfer. In this case, your rear brake will be more effective because it has more static load on it due to the geometry of the bicycle. On any surface where you can generate sufficient braking force to cause the front tire load to exceed the rear though (which I'd expect to be on most surfaces except snow/ice), the front will be the more important brake for stopping.