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Single monolithic model, or separate models?

One of the issues that arises when multiple audio input/output options are available is whether, theoretically, it is better to put all the eggs in one basket or to keep them separate.

Take a household multimedia centre. The user could have a range of options from bluetooth wireless to wired USB or wired into the MB headsets, each of which offers different advantages and disadvantages, quality of audio, portability, etc.

You have two options, build the SRE model using all the headsets equally, modifying the single monolithic model so that the same model is used for recognition no matter what headset is chosen. Alternatively, build separate models for each headset and run that specific model when expecting good recognition, keeping the model pure to the quirks of that headset.

Are there any reasons to expect better results from the one approach or the other?