As for how grit compares, I can't say. But, the abrasive used for the synthetic sapphire will be much harder than the Arkansas stone. If you're trying to sharpen (polish) one of the more modern stainless steels, the sapphire is likely to be more effective. Especially, as has been pointed out, by using very light pressure. That, by itself, can make a big difference.
The hard Arkansas stone can polish carbon steel edges nicely, but won't be as effective on newer, harder and more abrasion resistant steels. I have a nice little black Arkansas pocket stone, but haven't used it much, because it's effect on modern stainless is almost negligible. It did do a decent job on a carbon-bladed Opinel I recently touched up.