My response is for 1911s only as I have never owned a Sig or other pistol with a hammer.

Cocked and Locked is the only way to have your 1911. Hammer cocked and safety engaged with a round in the chamber. If the hammer is down and round in chamber, you must manually cock it or if no round int he chamber, must cycle the slide to chamber a round and those two options are difficult to make happen when you need to get rounds down range in an attack or emergency with a POS trying to kill you etc.