Simple solution: compare the relative humidity
The relative humidity is the major determining factor here! To be more precise, the lower the RH, the more quickly water will evaporate into the air, so you want the environment with the lower RH (as a percentage).
There are several factors that can affect your decision, however:
Interestingly, RH is temperature dependent-- hence the term relative humidity. RH is a measurement of how much moisture is in the air vs. how much it could have. The warmer it is, the greater the absolute moisture content can be in the air. Therefore, if you start off with a house where the temperature and humidity are the same throughout, you could reduce the RH in one room by raising the temperature with a space heater, stove, or fire. Outdoors, barring weather fronts, you are more likely to encounter changes in temperature and RH that follow the time of day. (Make sure you don't leave clothes out overnight or water can condense back on them if it gets colder than the dewpoint, which is when the RH hits 100%.)
Air movement also makes a big difference. If there is no air current the air containing the water vapor will remain close to its source, with the result that the wet clothes will be surrounded by a zone of high RH and therefore cannot continue to dry at the same rate. Usually there is much more air movement and therefore air exchange outdoors.
Air conditioners prevent spikes in RH inside your house by collecting condensed water from the air as it is cooled down, which means that it is constantly drying out the air in your house-- but it usually just keeps the RH constant because the temperature is dropping.
Clothes spread out for maximum surface area and air flow should dry eventually in either environment, but not so well, e.g., in an indoor swimming area or locker room with tons of showers in constant use-- the evaporation of those water sources will keep the RH elevated. A minor consideration: mold growth happens at high RH, but things need to be constantly damp for about 48 hours before it becomes a problem. If it's really humid indoors and out, consider setting up a heat source to dry out (lower the RH of) the air.
If you want to dry your clothes inside, you'll have the most success if you hang clothes in bigger, warmer rooms, leave doors open between rooms, and set up fans (or dehumidifiers, if you want to invest).
Experiment: which is best for your situation?
This changes with the weather, so you'll have to make a new assessment each time.
If you want to figure out precisely which is better for you via quantitative experiment, you can buy a cheap thermohygrometer to measure the RH in your house. (Here's one for $5 on Amazon, though I encourage shopping locally if you can!)
You can place it in the space where you would dry your clothes and compare that reading to the published weather stats for the general outdoor RH that day and time-- or you can take your handy new hygrometer outside and get a new reading for comparison (give it a minute to adjust). If they're not wildly different, you'll probably get faster drying (not to mention a little bit of natural fabric softening) where there is more of a breeze.
You can also try a practical experiment of drying clothes inside and checking the RH next to them as they start to dry-- the space they are in will probably increase in RH a bit unless you have good air movement; if your indoor drying space gets much too humid you might set up fans for circulation, or just plan to dry clothes outdoors.