I use a Lightning camera adapter (USB port) to an external DAC and headphone amplifier. It gives me the best possible sound quality, since the audio is pure digital until it hits my DAC, which, I can assure you, is much better quality than any internal DAC included in a smartphone.

Personally, I don't really care about the headphone jack because I never use it. I will admit, I'm different than 99.99% of other users.