In a nutshell, Zoe’s Tale is The Last Colony told from Zoe’s point of view.
It definitely has a different feel to it than the rest of the Old Man’s War books, matching the idea that it was written by a teenage girl (having never been one, I can’t guarantee the accuracy, but it worked for me).
(Obin: “it,” not “he” or “she.” Because they’re hermaphrodites. That means male and female sex organs. Go ahead and have your giggle. I’ll wait. Okay, done? Good.)
On top of that, you do actually get a pretty decent chunk of storyline that John and Jane never saw–Zoe’s pretty sneaky when you get down to it. Honestly, it strains belief how much she gets away, but in my headcanon… Jane totally knew at least some of it. Works out.
Other than that, Zoe’s Tale has the same problem just about every ‘the same story from a different POV’ has: we already know how things are going to go. It’s hard to have anything that’s both surprising but still fit with how we know things have to go. That doesn’t make it bad by itself–I really enjoyed Ender’s Shadow for one–but it does have to work harder. And Zoe’s Tale doesn’t quite make it.
Unless you’re a completionist, you really could skip Zoe’s Tale and just be done with The Last Colony. Not a bad book. Just not necessary.