One thing I find myself regularly running into in the games with Pairup mechanics is that, when I'm repeatedly failing a map (losing somebody I like and needing a restart) it's commonly because I'm either pairing up too many units or not pairing up enough.
So, typically damage output will be higher when you've got your units separate, because everyone will get to do their own attack, and in the case of Fates you can take advantage of the attack assist stance. However, having units separate means they're not getting stat bonuses, and the squishier units are all exposed, so you'll take more damage if you can't wipe out all nearby enemies in one go.
Either way can lead to casualties - sometimes I've got too many individual units and can't kill every enemy, so my weaker ones get ganged up on and killed, but sometimes I've got too few attackers on my turn and I can't kill the enemies I needed to, and as a result they kill one of my units and I reset.
A few good strategies:
Lead an attack by charging in with two tough units paired up together, who you've calculated can survive the counterattack on the enemy turn (I find myself using Corrin and Xander together for this, because they've both got huge damage and durability). Then, on your next turn, send all your troops in to wipe out the cluster of enemies. Fairly standard hammer/anvil.
Plan out where you want your units to make their attacks from in order to maximize the use of pairup attacks. This works well with the top one, but a good strategy is to go in with a paired up unit in Guard Stance (who can't get assist attacks anyways), then send everyone else in, one-by-one, each moving up next to a friendly unit and attacking. If you make good use of units with aura skills, debuffs, and area damage skills, you can easily wipe out all of the enemies in a region and not get counterattacked on their turn.
Don't always split up your troops. In a lot of maps it seems like there are two clear first areas to go to that are near the starting zone, so I figure I should send half my troops to one and half to the other. It's frequently feasible to get both at once, but when your troops are stretched too thin you cannot afford a screwup or unlucky attack, so it's sometimes best to just take your time.
(This stuff is mostly relevant for the 3DS titles, and even then YMMV. )