It's difficult to determine, before shooting, which load will have more "felt recoil."
Free recoil energy is a number than can be calculated, but it's only a number. Felt recoil is much more subjective, it's the entire picture that the shooter experiences when he drops the hammer. It can be wildly influenced by many, many factors, and the only real way to get the answer is to shoot them and FEEL them and determine at that point what you think.
One of the differences that is common is the blast experience, which can be larger with a lighter bullet load. The concussion coming from the flash gap (between the cylinder and forcing cone at the rear end of the barrel) and the blast coming from the muzzle add to the experience of "felt recoil", and the blast often feels more stout from a lighter bullet load. And then, shoot the SAME load on an indoor range (where before you'd only ever shot outdoors) and the close quarters may make the entire experience seem two-fold.
If you are certain that you simply do not care for or handle recoil all too well, consider that the revolver you own is a bit of a firecracker! However, being a .357 Magnum... it can safely and happily digest any/all/every .38 Special load on the market. And .38 Special, even the hottest available, runs at around half the pressure of the .357 Magnum, so it may almost feel like shooting two totally different handguns.
Differences in 125gr and 158gr .357 Magnum rounds?
One difference you may see is that the two loads hit in a slightly different spot on the target. Windage should be the same, but the elevation is often different between the two. At 7 yards, you probably won't see it. And if you aren't a particularly good shot, you may never get a good handle on it. But if you put the revolver on a solid rest and shoot a good distance (say, 15-20 yards or more), you should notice an elevation different in where they hit on target. This is something -FAR- easier to notice when comparing .38 Special and .357 Magnum loads than it is when comparing 125 vs 158gr loads in .357 Magnum.
Another difference that has been noted -- the 125gr .357 loads tend to be more "harsh" to the revolver itself. I've heard it explained as the result of the SHORTER 125gr bullet exiting the face of the cylinder more during the absolute peak of the burning inside the cartridge, allowing far more flame & blast to smack the bottom/inside of the top strap of the revolver.
It's LONG been a topic of discussion that 125gr .357 Magnum loads "beat up" revolvers more so than 158gr .357 Magnum loads, but this is an issue with a lot more discussion (and vigor) than it is with hands-on evidence and proof.