Verbose mode on 
The difference is in the way the number of samples will be determined. When using local subdivs, the image sampler’s max subdivs value is taken into account. When a light (for example) uses 8 subdivs and the image sampler is set to 1/4, the samples for the light will be 8 subdivs = 8*8=64 samples but divided by the sapmler’s 4 subdivs = 4*4 = 16 samples, so 64/16=4 samples for the light. Increase the light’s subdivs to 16 and you get 16*16=256/16=16 samples. Increase it to 32 and you get 1024/16=64 samples.
Now why does V-Ray divide the local subdivs by the sampler’s subdivs, well - to prevent taking way too much samples (that was the original design) and slowing down the render too much.
Then came the “divide shading subdivs” checkbox. Disable it and all that maths will not happen, so essentially with “divide shading subdivs” = off, and for the same 32 light subdivs you’ll get 1024 samples.
In the above setups the min shading rate will determine the ratio between AA and shading samples per AA rays, essentially to bias the sampling towards more AA or towards more shading samples. I would probably need to run some tests to get you some exact figures about this, cause I’m mostly making this up (I haven’t really tested such a setup for years since the min shading rate = disable local subdivs options came to V-Ray).
The beauty of setup simplicity, though, comes when “use local subdivs” is off and you only play with the image sampler’s subdivs and the min shading rate.
In brief, it would mean for image sapmler 1/4 and shading rate 1 >> 1 shading sample for each AA ray, i.e. for the pixels where the sampler has reached its 4 subdivs or (4*4=)16 samples, there will be 16 shading samples for each shading effect (16 for lights, 16 for reflections, etc). Increase the shading rate to 6 (the default) and you get 6 shading samples per AA ray, or for the pixel where the image sampler made the max 4 subdivs, you get 96 shading samples per shading effect per pixel (4*4=16 aa samples and for each of those you get 6 shading samples).
I should note that the above examples rely on no adaptivity, i.e. I’m relying on a theoretical case where with 1/4 image sampler subdivs the image sampler actually manages to make the max 4 subdivs (16 AA samples) per pixel.
With all of this said, in a case where you want to clean reflection noise coming from a specific object, what matters most is your initial setup.
* If you initially have setup V-Ray to use local subdivs and divide the shading subdivs to the sampler’s subdivs, then you will have to take that into account and when increasing the object’s reflection subdivs keep in mind that they will be divided by whatever your sampler’s max value is. So you might need to not simply double them, but triple, quadruple them and so on. Bumping up the subdivs mult in the VOP node (vrayObjectProperties) will just multiply them too to the same effect.
* If you’re initially using local subdivs, but not dividing them to the sampler’s subdivs, then no math is involved - just up the reflection subdivs or up the VOP’s subdivs mult. That will simply mean more samples.
* if you’re using the defaults - use local subdivs = off, then the VOP’s subdivs mult will multiply the min shading rate value for the pixels that your object takes up. It will result in more samples for not only reflections, but all shading effects and probably make V-Ray oversample those pixels, but it is really simple to do. Also, V-Ray has become quite smart in recent years, so I’d expect it will know what to do (I have been consistently failing to trick it into behaving in a less adaptive way than it is by default).
This might shed some light onto why the new default is better (I think it is, use local subdivs = off and tweak min shading rate) since less math is involved and less things to consider when tweaking the render settings.