It's all about what is best and easiest for you... which generally creates the conditions for healthier birds. Quail are highly adaptable and both will work. Where I am we actually have four seasons, and we leverage the seasons to help create an optimum bird environment. I love having my birds inside, because they are protected and are in a very stable and convenient environment... the trade-off is the intensive cleaning and costs in space and utilities. Raising birds outside is generally easier, because it is more manageable to clean and maintain (and the sun and wind have amazing health benefits). There are many more reasons to raise birds on pasture with (daily moved) quail tractors. Regardless: having modular pens and/or cages can allow you to have the best of both worlds.
If you were to raise them inside, I would encourage you to give them a dedicated 'space' where nothing else really is. A simple partition can go a long way.