I am currently in the process of writing a mission system for my game, and started questioning if I should adjust it, and make it into a quest system.  

Missions: like GTA and assassin's creed. While you're working on a mission, you can't start other missions. 

Quests: like World of Warcraft and Skyrim. You've got a bunch of people asking you to do things, and you decide when to complete each one.

Obvious pros and cons: quests give you more freedom and allow you to more efficiently plan your journey, while a cluttered quest log can seem overwhelming, and make individual quests less memorable ('why am I killing these creatures again? Who asked me to steal this document?'). 

What are your thoughts on the gameplay implications of quests vs missions? Do you enjoy the focus of having one objective, or do you prefer the freedom of completing multiple quests at once?

Have in mind that mission system is like that because you wouldn't be able to make some kind of missions as quest-like stuff. I mean, lot of missions from GTA are like "chase that dude with your car, shoot at him, when you kill him get the helicopter and so on". They are scripted missions with constrains and events, it is not that easy as "kill A" or "get x20 B items".

Maybe you could mix mission and quest stuff like MGSV does, you can run freely on the map, but when you reach a certain radius, game will ask if you want to start "X" mission.