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Is the left circuit equivalent to the right?  If all my devices are connected to ground (nothing goes from 12V to 6V), does the switch placement matter?  I'd prefer to only have one switch, but I'm worried I may be building up a charge in the positive line which might affect my devices, I'm unsure.
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It's not exactly equivalent because you could close the 12V switch (on the right) while leaving the 6V switch open, or vice versa, unless you ganged the switches together to always open/close at the same time.

Otherwise the switch placement doesn't really matter. There is no issue of "building up charge".

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Is the left circuit equivalent to the right?  If all my devices are connected to ground (nothing goes from 12V to 6V), does the switch placement matter?  I'd prefer to only have one switch, but I'm worried I may be building up a charge in the positive line which might affect my devices, I'm unsure.

Yes, as long as their is no load(s) wired between the +6 and +12 then a single switch contact on the common negative wire will stop all current flow and can be used as the main power on/off switch. However it's more 'conventional' to switch the positive rails. You could of course use a single switch that has dual contacts (DPST or DPDT) that would switch on/off both the +6 and +12 with a single switch.

example: http://www.allelectronics.com/make-a-store/item/SMTS-8/DPDT-ON-ON-SUB-MINI-TOGGLE-SWITCH//1.html

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I suspect your 12V and 6V circuits are connected by more than just power wires - if so then using the single switch could cause problems as current might then flow from the 12V stuff via signal wire(s) to the 6V stuff (possibly causing damage).  A dual-gang switch would be the conventional way to handle this.
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NO - they are not.

Imagine if you had on both circuits lightbulbs (on a 12 volt bulb, the other a 6 volt bulb) running from the 12 and 6 volt sides, with the other side of each lightbulb going to ground to -complete- the circuit. In the case of the circuit on the right, the switches would each control a lightbulb, allowing you to turn one or both on or off at the same time.

However, with the circuit on the left, when the switch is open, current from the single "top" 6 volt battery would flow thru both bulbs (and the bulbs would be dim), because of the completed circuit thru the ground return path. When the switch is closed, the bulbs would still be lit, but running at their normal brightness.
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Thank you all for the feedback, I'll likely go with the left system for now, though I may look into a dual switch at a future date.

The application I was looking at was using the 12V to drive motors (and the Ardunio 2560) while the 6V would be stepped down to 5V to supply the necessary current for my webcams and router.  Thank you for pointing out the potential for reverse current flow, that could have definitely been a significant problem, I'll have to see if I have any appropriate diodes I can incorporate into my design regardless of the final layout...
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