is it better to run my inline fuse next to my car battery or near my amplifier?

If you install the fuse closer to the battery you also protect the system from a short in the cable.

If the cable gets pinched or the insulation rubs through, and there is no fuse you can short out the battery and cause a fire, with no fuse to cut the current. If the fuse is close to the battery, it also protects the cable by blowing, so no melted wires or exploding battery.

Makes no difference to the amplifier where the fuse is sitting.

You know the purpose of a fuse or circuit breaker? It is to protect the wiring, not the amplifier or any other device. The fuse should be close to the battery.

Assuming you have a dedicated circuit directly from the battery to amplifier, it would be slightly better installed at the battery. That way it would protect both the circuit conductor as well as the amplifier.