Actually a switch mode power supply is usually a lot better than the old transformer for voltage stability. It continuously adjusts output to compensate for load and input voltage so is very stable. Because they switch in the order of 40kHz it is easier to smooth out the resulting voltage requiring smaller components. They are not as reliable as a basic transformer but are very easy and cheap to replace. Either way the additional voltage regulation in the device will cope with either. Things that are likely to have a greater influence of repeatable accuracy will be temperature variations, draughts, vibrations/movement and static charge build up.
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