...a .22 mag will defeat most body armor.
If you don't bother with the shape of the bullet (round nose / pointy nose) and bullet deformation (and deformation of the material you shoot at), what determines if a bullet will penetrate something or not is roughly if it has enought (kinetic)energy per area.
The formula for kinetic-energy per area is:
E/A=(1/2)*m*(v^2)/(phi*(d/2)^2)
where m is the mass of the bullet, v is the velosity and d is the diameter.
and using this formula I can find the velosity a .44 must have to penetrate the same as a .22 (where thjey have the same E/A)
asuming: .22mag: m=0.003 [kg] , v=600[m/s] , d=0.0056[m]
.44mag : m=0.020[kg] , v=what we want to find, d=0.011[m]
the velosity of the .44 will be:
v= Sqr.root((0.5*0.003*600^2*0.011^2)/(0.0056^2*0.5*0.02)=456.5[m/s]
I don't know if 456 [m/s] is about normal for a .44mag but if it is, the two will penetrate about the same. ( but the .44 will probably do more demage on the other side of the penetrated material)