I think more voltage is better because it seems to favor the gold to gold chloride reaction more. But once you get over a certain point, the difference is small. I say go constant voltage and let the current change within the limits of your supply.
Here's how I think of it:
Gold electrolysis has several processes going on simultaneously.
Suppose you have two processes in your cell, A and B. B is the one you want, but you also have to do A.
A requires 2 volts, and B requires 3 volt at a minimum to energize.
If you ran your cell at 2.9 volts, you would only get reaction A.
If you ran your cell at 3.1 volts, you would get mostly A and a little B because the overvoltage for A is 11 times bigger than for reaction B.
Now fire it up to 30 volts. The overvoltage for A is 28, and th overvoltage for B is 27, so they are almost equal.
This is what I think goes on. With silver, any possible reaction makes silver compounds, but with gold, only one does.
Other things also affect the ratio of the reactions, like the quantities of the reactants.
Gold is just a lot more complicated than silver