Big difference for most a/c is that the front wheels typically only carry about 10% of the total weight (or less) statically; your car is more like 50-50 usually.
Then the long "arm" to the wheel means that any pitching down caused by braking on the mains can be resisted with proportionally less load on the nose.
A very few aircraft have used brakes on the front wheels (SAAB Gripen is one IIRC) but most don't bother.
Think of it as a similar case to a drag racer - small spindly front wheels because all the weight is near the back wheels.