Resistor on anode or cathode?
There's no difference. 

One of the basic principles of electric current is that the same current flows through all elements that are arranged in series.







simulate this circuit &ndash; Schematic created using CircuitLab

The purpose of the resistor is to limit the current, it doesn't matter in which part of the circuit it is located. 

In the case of throwies, the internal resistance of the coin-cell battery is used as a current limiting resistor.







simulate this circuit