This work investigates the noise characteristics of filamentary- and interfacial-type RRAM devices in a single material system based on La2NiO4+δ, using low-frequency noise spectroscopy across different resistance states, read voltages and device sizes. We observe a clear difference in the noise properties of the two device types: (i) filamentary devices exhibit overall elevated noise levels compared to the interfacial ones, (ii) the relative noise magnitude between high (HRS) and low resistance states (LRS) in the two device types is inverted: elevated noise is present in the HRS of filamentary devices and in the LRS of interfacial ones and vice versa, (iii) no area dependence of noise properties is observed for the filamentary devices, whereas interfacial devices show a size-dependent frequency exponent and noise magnitude scaling. For both switching mechanisms, a systematic two-stage noise suppression with increasing read voltages is observed, which is found to be correlated with the transition from ohmic to space-charge-limited conduction. Our study links noise characteristics to the underlying switching and conduction mechanisms of oxygen vacancy migration-based memories.