Pretty much any gun except a .22 will have more recoil than a .25.
Below are some reasonably small guns in different calibers for comparison. For each one, look just below the picture of the bullet and find where it says "Recoil Factor." That shows the theoretical amount of recoil for the gun. So, the recoil of the .22 listed would move a 0.26 pound weight a foot, the .25 would move a 0.61 pound weight, the .380 would move a 3.69 pound weight, and the same gun in 9mm would move a 7.72 pound weight. That will only start to give you an idea about recoil.
.22 Ruger SR22
.25 Heritage H25
.380 Ruger LC380
9mm Ruger LC9
Here's the Kel-Tec your friend has offered, which has nearly as much recoil as the 9mm Ruger above (and would sting your hand more because the recoil is fast and sharp).
.380 Kel-Tec P3AT
Finally, a big, heavy gun to show what extra weight does to reduce recoil.
9mm SIG P226