Maths!
10 ranged power = 10% more damage.
10 doubleshot = 10% chance to hit twice (lets say double damage for simplicity)
In the simplest form, they are equal (assuming everything else is equal too, no different scaling, damage numbers are consistent, what you are fighting has no reductions, etc)
If you do exactly 100 damage per hit, and attack 10 times, with only 10 ranged power, you'll do a total of 1100 damage.
With the exact same perameters, but you only have 10% doubleshot instead, after 10 attacks you will, on average, also do 1100 damage.
The difference is 10 ranged power is consistent for all attacks, while 10 doubleshot is only a chance to apply and thus comes in bursts but doesn't apply all the time (only 10% of attacks will get those benefits). Even after 100 this still applies, as 110 doubleshot is a guaranteed double, with a 10% chance for triple. While 110 ranged power is always 110% more damage. The maths (assuming perfect averages over time) ends up remaining the same.
The theoretical best is to keep them equal. Of course, if one is easier to get a lot of, it's still worth getting a lot of it.
edit: and as Lominal said, if you can only choose one, and one is lower, it's better to bring the lower one up. Another consideration is that doubleshot will multiply all other effects of a hit, while ranged power only affects what it affects, usually the initial number, maybe imbue damage as well. (though the other effects of a hit are usually quite minor in the grand scheme of DPS).
Basically, the more variables and effects you have, the more complicated it becomes and things can shift. But at the most basic, they are equal.
edit: later in this thread some of us go into greater detail, while arguing about the validity of AI and using AI with incorrect data and assumptions