The sync stripper isn't necessarily any better at extracting the sync from the composite video signal than the display device is.
There are only two reasons to want/use csync. First is compatibility, where you have a display device that only supports csync. Extron devices are an example of this, they often require pure csync. Second is quality, where you want to avoid having interference caused by the use of composite video sync.
One big problem is that sync strippers are normally put in the SCART head, which is at the end of the cable. When you're just looking for csync for compatibility reasons, that's fine. But from a quality standpoint, it's a problem.
The reason why composite video sync causes quality problems is because the composite video signal running down the sync wire can couple with the video lines going down the same cable. This is called crosstalk, where a signal going down one wire causes interference in another wire nearby. Over time, people have sort of equated this to "composite video sync = interference, csync = clean, so composite video sync bad", but this is an oversimplification that leads to a faulty assumption: that putting a sync stripper at the display end of the cable helps at all with that.
The problem there is, if you strip the sync *after* the signals have gone down the cable, the damage is already done. The composite video signal went down the cable, coupled with your RGB lines causing interference, and then you stripped the sync off. You end up with a "csync" cable that still has interference! It's also worth noting that it's the chroma burst (colour signal) part of the composite video signal that causes the interference, which is why you don't see this problem with luma sync despite a luma sync signal being so similar to composite sync with the only difference being the luma sync signal has no chroma burst.
There are two workarounds to this: strip sync before going down the cable, or use individually shielded (or coax) cables. Stripping sync at the start is tricky because there is very little room in the console plug end of the cable, so you almost need to do that inside the console before it gets to the output port. The other solution of extra shielding works, but results in thicker/stiffer and more expensive cables, but it's still a viable solution.
So, back to your situation: the SNES Mini. You're adding in an RGB amp (hopefully Voultar's RGB bypass board, it's great), which means you've got csync already at the console. What you really ought to be doing is to use the csync off the console. If you can modify the console end of the cable for that, great, otherwise you should probably just get a new cable. The only scenario where you should be putting a sync stripper in there is if you're using a device that absoluetely requires csync.
For the resistor, I'm speculating here because I'm no expert, but I believe you only need to do that if you have TTL sync going down the cable. That is, if the csync signal is already properly attenuated 75ohm, you don't need it. If you can modify the console end of the cable to connect to csync, and you're using voultar's board, then it has a solder bridge that you can leave disconnected to have it output 75 ohm csync.
If you're using a sync stripper, I guess it depends on which one, but the LM1881 datasheet (
http://www.ti.com/product/LM1881/datash ... NLS3848426) seems to list 0.2 to 0.8 volts, which seems to indicate it's not TTL and therefore does not need the resistors... Somebody who is more savvy on this sort of detail could correct me if I'm wrong?