"Father's Promise" was the first TWoM DLC that I played. The premise of being a father having to take care of his sick daughter was an interesting one. Sadly, I felt rather underwhelmed by this DLC. Playing "Fading Embers" afterwards further highlighted the downfalls of FP because FE was so much better. Like other people have mentioned, there's not much survival mechanics in it because the story is so short that by the time you've set up a good base, it ends. Which would be fine if the story was well fleshed-out, but it's not, really. It's intended to be a tearjerker, but it's very simplistic in the way it achieves this. TWoM sometimes has a tendency towards this, taking a very obvious approach to their moral lessons to the point where it sometimes feels like the game is taking your hand and pointing out: "This is sad! Feel sad, player!" Usually, it's not so bad that it feels TOO overt, and of course the subject matter usually is very sad, but FP tips over that line (in my opinion). It took a very simple and obvious approach to its storyline, which I was a bit disappointed by. There's also no multiple endings or any kind of divergent pathways. The story is very linear. I much prefer "Fading Embers" due to its more complex approach to the moral questions of its storyline, and its branching pathways/multiple endings, so my suggestion is to buy that instead as it's definitely worth the slightly higher price over "Father's Promise".
"Fading Embers" is its own little story about a woman called Anja (and companions) and how they must weigh up what's more important: Saving works of art and other significant cultural items, or surviving? I played this after "Father's Promise" and this is much more elaborate. Multiple endings, and plenty of difficult decisions that test how much you're willing to set aside your morals for survival, or whether heritage is more important than helping those in need, etc. It's significantly longer than FP and I like the party characters, following This War of Mine's trend for having very "real feeling" characters with interesting backstories. The characters will judge your decisions so there are rarely any "perfect" choices - someone will always disapprove. This makes the decision making process a lot harder and I had several moments of going "Arrrghh!" because I just couldn't decide. It also adds some new mechanics like talking with NPCs and having the party members talk amongst themselves, which adds a little extra to the characters. A good addition, much better than FP, in my opinion.