Pros for wired: better fidelity, no batteries to charge, lighter weight, more headphones to choose from, cheaper headphone options, no adapters to lose, can listen to music while charging.
Another pro for wireless is that you get more space inside the phone, which means more room for chips, batteries, etc. And you have to consider things like headphone jack make it harder for your phone to be waterproof since that's one more place you have to figure out how to seal.
