From the early sections of the game all the way through the Makeb story, the story aspect of instanced missions worked one of two ways. For our class story-line instances, the owner would make all the story decisions, while the other player would see the cutscenes but not have any control. Only the owner got credit for mission completion, which was fine since the other player didn't have the mission anyway. For all other instanced missions, both players would be able to make decisions, and the game would randomly choose one choice. Both players got credit for completing the mission instance, no matter whose choices were chosen. It worked fine, and allowed us both to progress the same missions without having to do everything twice.
Once we started the Shadow of Revan expansion content on Rishi, though, this was no longer the case. The instanced planet story-line missions took place in something called a "Personal Phase", which meant that it worked like the class story-line missions. Only one player was in control, and completing the mission only counted for that player. If we wanted to go through the story-line together, we either had to do everything twice, or separate every time a mission instance showed up. We could still do non-instanced content together, and when a Flashpoint came along that was still fine, but all the other mission instances forced us apart. If that was a rare thing it might be OK, but those mission instances show up a lot, and several of them are fairly long.
Moving on to Knights of the Fallen Empire made things even worse. Almost everything you do until reaching Chapter IX is in an instance. You can summon another person into your instance, but again they can't progress their story. Worse, the second person misses a lot of the content: cutscenes start without them, and they can't hear side comments from companions and other characters. The second person also gets kicked out of the instances regularly, so the owner has to redo the summoning. It's a terrible implementation for grouping, so much so that when the patch notes say "We've made it even easier for you and your friends to play Knights of the Fallen Empire together" I'm tempted to call it false advertising.
Even after reaching Chapter IX, actually playing the game as a team is nigh impossible. The new conversation format only allows one player to participate at a time, and those "Personal Phase" instances keep cropping up. The entire Odessen command center bunker is inside one! Heroic missions and Flashpoints are still workable for a duo, fortunately, but not all the content is set up that way.
I sort of understand why the SWTOR designers chose to go this route. I get that it allows each character's story to unfold separately, and that it makes story-writing a whole lot easier. But it also means the game is a long single-player chain, which players can't enjoy together. Back when I first went through Knights of the Fallen Empire, I said that it felt like watching a movie. But at least you can do that with a friend. This is more like each watching a show at home, only able to talk about it afterward. After you finish that long chain, then you can play together in repeatable Flashpoints or heroic missions, but at that point the game is primarily just an MMO grind exercise, not a story to follow.
I'm pretty disappointed in the way things have worked out for our duo in the recent content. One of the best parts about playing as a duo is seeing the story unfold together, and talking about things as they happen. It's really difficult to keep that going in the newer content. L and I may still go back to earlier content, particularly with a couple of Imperial characters of classes that we haven't tried yet. But when SWTOR releases new stuff, I'm afraid we'll each be going it alone.