Does stopping the same bike and rider at the same velocity with the front brake require less energy than the back brake? It's the same body made by the rider and the bike moving at the same speed. So, even though braking on the front/back alters the normal forces on the opposite wheels thus creating more friction with the ground (if you back brake), you're still converting the same amount of energy to heat, correct? 
In other words, brakes made from the same material on the same wheel should experience equivalent wear if each one converts X Joules of kinetic energy to heat energy, no matter if they are applied on the front or back wheel?
 A: The answer depends on whether the wheels skid.
When you brake with just the rear wheel, it's quite possible to skid; if you apply the front brake, the increase in normal force on that wheel tends to prevent skidding (although in extreme cases it could make you fly over the handlebars).
Applying the rear brakes hard enough to block the wheel would generate little wear of the brake system, and lots of wear on the back tires. The same thing would not happen at the front.
In practice, which brakes wear more really depends on how much you use them. For motorbikes, it is recommended that you use the front brake more heavily to prevent skidding - in fact some bikes have a mechanism that pretty much ensures this.
But from a pure physics perspective, the kinetic energy that needs to be dissipated is the same, regardless of what brake is applied.
A: It doesn't matter if the brakes are the same.  The bike+rider has a certain kinetic energy.  If you stop it, you need to dissipate that much energy. The problem with braking the rear wheel is that braking reduces the load on the rear wheel making it prone to skid.  If you brake gently enough, the wheel will not skid.  You will then dissipate the kinetic energyin the rear brake just fine.  Even if you skid (as long as you come to a stop), the total energy dissipation is the kinetic energy at the start.  If you skid some of that energy may be dissipated in a fall, but that is a bicycling problem, not a physics problem.
A: 
you're still converting the same amount of energy to heat, correct?

Yes.

In other words, brakes made from the same material on the same wheel should experience equivalent wear if each one converts X Joules of kinetic energy to heat energy, no matter if they are applied on the front or back wheel?

I don't know.
Why do you expect that "wear" is directly proportional to "heat" or "energy dissipated"?
If I don't brake as hard, and therefore take longer to stop, is that the same amount of break wear?
A difference between the front and back may be that because the front is less likely to skid therefore you brake harder and stop more quickly. It's the same kinetic energy dissipated (more quickly) but I don't know whether it's the same wear.
Wear is clearly a complicated topic: Wear.
Here's one theoretical example of a non-linear relationship between energy and wear: if the braking is rapid then the heat doesn't have to dissipate, therefore the temperature increases, and therefore (if the brake's material softens at high temperatures) the wear increases.
I say 'theoretical' because sfaik bike brakes don't get hot enough to cause much brake pad 'fade' (in an extreme the heat is more likely to explode the tire if it's a rim brake, or boil the hydraulic fluid if it's a hydraulic disk brake).
A: Actually, if you apply the front brakes, there is a tendency to topple, while if you apply the rear brakes, there is a tendency to skid.
Now, as the linear momentum is converted to angular momentum in this case, by an impulsive brake force, there is some loss of energy. Also, the time of contact of the brakes is less. That is why applying the front brakes requires less energy, because the toppling tendency is outweighed by the system's weight.
