When my darling girlfriend and I hike together, we always cook separately on our own alcohol stoves and I highly recommend it.
Advantages:
-We can each cook what we want, when we want. Even so, nothing stops us from sharing meals together, we'll just cook our own meals at the same time if we like. Sometimes it's the same thing at the same time, sometimes not, but we're always happy.
-If we want to hike separately for a short while, or say if I want to push on for a potential great sunset spot and she wants to call it an early day, we aren't left with the dilemma- Who's going to be eating Clif bars for dinner?
-We're both weight concious, and carrying our own separate systems eliminates some issues. If she wants to carry slow-cook foods and I'm doing couscous and potato flakes, I'm not irritated sharing the weight of a bunch of extra fuel to cook her stuff.
-Cooking our own food makes planning easier in some instances as well. Say when assembling a big maildrop for the both of us, it's easier to count calories when I don't have to split the caloric value of a food item between two people.
My $0.02.