In my limited experience so far of playing (11h) with a mixed party of both, I've found that the companion side quests are the only thing you'd really miss.
However there are some companions you'll meet along the way who do add to the storyline by allowing you to interact with them to talk about the primary story points, what or who they are, background information and how they affect both you and the world around you.
I've found this added a good deal of context to the story and helped to flesh out the lore of the world, giving my actions in the game more meaning.
So overall, I don't think that you'd miss to much, but it's my feeling that the game is designed to be played with companions mostly, in order to provide a more complete experience.
It's also worth noting that you can swap out your players at an Inn, so you could play a difficult dungeon with your best party, then head back to the Inn and swap in a companion to the team to get their side quest, although I've not tried this yet as I don't have any 'spare' team members.
Yes, there is a tickbox in the game options menu where you can toggle this on and off.
An afterthought; but worth mentioning. As you move the difficulty slider, the checkboxes will update to match.
Best Answer
According to in game book, The Iroccian Calender, a day in Pillars of Eternity lasts 27 hours.
Source: http://pillarsofeternity.gamepedia.com/Anni_Iroccio