I've finished the nine chapters of Fallen Empires that were released. Shintar makes a good point, when she describes the experience as "the borders between your personal story and the rest of the game are marked more starkly." The main story is very much a true single-player experience, the KotoR 3 that people have been asking for.
But after that come the more traditional MMO elements. Here, Bioware has done some interesting things. The main story of Fallen Empire is not complete yet. What's been released is more like Part 1. Where it stops, your character is setting up an Alliance to oppose the Zakuul Empire.
In some respects, it's like Garrisons from WoW. Only the focus is on recruiting new companions, and sending you out into the galaxy to accomplish things, rather than encouraging you to hang around your base.
One amusing element is that SWTOR now has a second conversation style. Bioware is touting it as a callback to KotoR, but it's real advantage is that your character is unvoiced. This allows Bioware to add these small pieces of content without calling in all 16 class voice actors.
In any case, there are 4 or 5 companions you can recruit through small missions or other tactics. For example, one companion requires you to participate in 20 PvP matches (wins count as 2 matches). Another companion requires you to hunt dangerous beasts, which you can do by killing World Bosses. Level sync makes that a lot more interesting. I like this because the only reward is a companion, of which you have plenty. So these missions are totally optional.
There are also Star Fortresses. Six worlds have Star Fortresses in orbit, and you have to do a mission on the ground to take out the shield protecting them. The Star Fortresses themselves are miniature instances, which can either be done solo or in a group of 2-4. It's pretty great content for just grabbing a friend and running through them.
Finally, all the planetary Heroic missions have been rebalanced and are available from your base, offering transport directly to the mission. This is essentially solo or duo content, and rewards lockboxes which you turn in to improve your base, and also gives you legacy cosmetic gear.
All in all, the Alliances seem like a strong and extensible system for solo and duo endgame content.