I have to admit, I am not the complete firearms expert, but I do see the value of having a rifle and handgun chambered in the same caliber. Having a setup like this, especially in a bug out situation, would be ideal.
In the old US West, cowhands would carry a single action pistol and rifle in the same caliber. It made sense as brass ammunition was heavy and carrying to many loads would be a pain. A popular shooting sport, Cowboy Action Shooting, has the standing rule that all participants must use a rifle in a pistol caliber and generally, the same as their competitive handguns.
Having same calibers makes sense in a bug out situation. Having two 50 round boxes of ammunition in a bugout bag (BOB) weighs less than having two boxes of shotguns shells or multiple magazines for two different caliber weapons.
There are some good combinations out there. For instance, a .357 lever action carbine along with a six shot revolver can also chamber .38 ammo making this a fierce combination. A .357 cartridge from a carbine is effective for short distance game hunting and both weapons are effective against two legged predators as well. There are similar combos in .44 caliber which many are quite pleased with.
I have a couple of caveats about my choices. I prefer a rifle and handgun which do no require magazines. I also prefer weapons which do not attract attention from LEO such as military style rifles might. Further, I intend on avoiding as many confrontations as possible as part of my "lay low" strategy so a lever action or revolver fit into my plans.
The other attraction to the pistol caliber carbine is weight (less) and size. Having a rifle that can fit, unbroken, into a backpack has it's advantages. Lugging a 10lb + FAL along with ammo has its disadvantages especially when travelling on foot in rough country.
Now some will mention the advantages of having the rifle/pistol combo in .22 which is true and it lends to carrying much more ammo than any other situation. I agree, however, I prefer to have a heavier caliber for greater diversity in targets and effectiveness in results. YMMV.