You can use either, but the amounts will differ since corn sugar is 95% fermentable, and cane sugar (table sugar) is 100% fermentable. This calculator will help. There will be no difference as far as flavor or other effects on the end product. I've used both on and off for years.
(I am assuming you meant corn sugar when saying "brewing sugar")
I've always used the corn sugar(dextrose) that either comes with the kit, or is cheap-by-the-bulk at LHBS.
However.... If you spend some time looking around, you'll see many posts by people much more expert than me that use table sugar and swear that there is no difference. I would agree, but I'm lazy.
If you use table sugar make sure you use an online calculator because it is more potent than corn sugar. I made the mistake of not calculating for style and ended up with some serious gushers. Basically ruined a batch of irish red