Here are pictures of the forces being applied to each tire in a clutch disengaged (engine disconnected from transmission), constant-steering-angle situation, in an FF, FR, and RR (in that order):


In both of the front-engined vehicles, the front outside tire is being worked harder than the rear outside tire (And this is
without trying to accelerate or brake).
In the front-wheel-drive car, the front inside tire is also working much harder than the rear inside tire. In fact, the front inside tire is losing grip, and what is actually happening with the rear inside tire is that the wheel is starting to slightly lift off of the ground.
With the rear-wheel-drive car, the front inside tire is working
less than the rear inside tire, even though the front tire has lost grip and the rear is still working. This is because the FR is more balanced than the FF, and the rear tires are resisting the rear end's urge to follow its inertia and slide out.
The rear-engined, rear-wheel-drive car turns everything upside-down. Not only are both of the rear tires working harder than the front tires, the front inside tire has lost grip, and the rear inside tire is still holding on. The reason why everything has changed like this is because the front tires have much less weight to shift, and the rear tires have to do all the work by themselves to prevent the engine-and-drivetrain-burdened rear end from following its inertia and sliding.
Conclusion? The front tires generally work harder than the rears, since they are
shifting the weight of the car. The rears generally do less work, since they are only
preventing the shifting of weight. The opposite holds true with RR cars, since the weight is in the rear of the car, the burden of keeping it in place is higher than the burden of shifting the weight in the front.