It's all about whether or not the game is CPU bound or GPU bound, and this varies on a per game basis.
If the game is GPU bound, your 6300 shouldn't be an issue, and an 8xxx isn't likely to give you significantly better performance.
If the game is CPU bound, an 8xxx CPU may give you better performance, and it's just as likely not going to as well. You'll see better performance if, and only if the CPU is clocked higher or the game can use the one extra module.