You need to know your body and abilities, and gear inches is one area where you don't have to guess. Use an online gear inch calculator to calculate the range of your current setup, then do the same for your proposed compact double.
I currently run a touring triple with a 12 - 27 road cassette. My easiest gear is a 26 - 27, or just a bit smaller than a 1:1 ratio, or 26 gear inches, and a big gear of 4:1, or 108 gear inches. If I were to switch to a compact double, I would have to go with a 12 - 36 to get the same low gear, but i would also have a bigger high gear.