I don't own either one but have examined examples of both. If I were to ever buy either one it would be the Papoose without a doubt.
However, I doubt that I will ever buy either. If I wanted a .22 survival gun, I think my S & W Model 317 revolver would be ideal. It is an eight shot, double action, adjustable sight, three inch barrel revolver. It is the Airlight model, weighing less than 10 ounces. It rides on my hip in a holster and is so light you forget its there until you need it. It never gets in the way of anything I try to do. Its small enough you can even conceal it in a medium sized pocket.
Another possibility would be my Ruger Single Six. It has both .22 LR and .22 mag cylinders with a six inch barrel. However it is obviously bigger and heavier. Also it is only six shot and is slower to reload. Just not as handy.
For a rifle, either my Marlin 39A Golden Mountie or my Ruger 10/22 would work. The Marlin's advantage is that it can cycle any standard .22 ammo (shorts, longs, or long rifles). The Ruger's advantage is that it is faster to reload with extra magazines and can use large capacity mags and is semi auto for faster repeat shots.
(Luke 11:21 KJV) When a strong man armed keepeth his palace, his goods are in peace:
(Luke 22:36 KJV) Then said he unto them, But now, he that hath a purse, let him take it, and likewise his scrip: and he that hath no sword, let him sell his garment, and buy one.