Why on earth would a 10k pot less accurate?
It will only give some more noise.
ADC's specify a maximum impedance of the signal. This varies by part and by frequency/speed. It really depends on the brevity of the sampling window, in case it is adjustable (as it might be on a micro). Most ADC are fine at 10K signal impedance in any scenario.
PIC micro ADC, for instance, have specified maximum impedance of 20K, IRC.
The only fundamental issue you (might) even need to take into consideration (power issue is IMO is just standard fare/issue; normal details) when hooking up two ADC to a single pot is that the ADC cap of each micro may be "opening up for business" after the last read/timed-discharge at the same time. There's a certain impedance of the signal coming out of the pot, and it may not be fast enough to fill both caps before the respective ADC's assume the cap is done charging. So the maximum impedance value that is listed for the micro should be derated. Else you may get a sporadic low reading in this event (not increase noise). Kind of like quantum physics, the act of measuring the signal will affect the signal. While being sampled, the signal will sag. The higher the impedance (in this case, the higher the value of the pot), the more sag you will get. Two measurements at once takes more juice to avoid clipping the reading.
Very much depends on what the application is, don't you think?
Yes, theoretically. But no, not really.
If it's a toy, go ahead and wire it up any way you like.
If this goes into an industrial setting, then you better do it right.
This is a pot. With variation in itself. Turned by a human. To make something happen. As long as you get the range and resolution you need and the result is consistent, the rest is just details. You have to keep things in perspective. But if you wanted the shortest sampling time and immunity to noise, and to remove as much offset as possible, you should maybe consider putting a voltage follower on the output of the pot. An amp with a gain of 1, or whatnot. A buffer. If the two micros should agree on a single value for w/e reason, then yeah, best to have the reading done by one micro and shared with the other. But devoid of that reason, there's no reason to rig up I2C bus just do to this.
When someone asks simple question like this with noobish schematic, 20 people want to give him specific solutions to problems they are only guessing at and which were never asked. Firewalker nailed it. You need a common ground. Done. I2C bus? Rotary encoders? Why not cover the fundamental issue at hand and let him figure out what, if anything, else he needs from there? If he had an I2C bus already in place, then he would already know how to share a couple bytes between micros. It's obvious he doesn't. He doesn't even have a common ground. Not all micro's even have I2C port. Maybe he should simply bit bang his own I2C instead of connecting a ground rail?