This is something I see going around right now, so I'm trying to organize my thoughts.
Right now I have Sweet Pea in her age grade- she is 6 years old and in the first grade.
I spent a lot of time last summer panicking about what level of work to give her because she was ahead of most Kindergarten programs I had access to. I never considered bumping up her grade, though.
This year she is doing a mix of work. Some of the things we are doing are not tied to a specific grade- history, science, and French are definitely in this category. The programs we are using are meant for general early elementary and are being successfully used by 1st graders and 3rd graders and even some older kids. I think that Bible and Catechism are hard to level, as well- it's mostly learning material (or gaining familiarity) and I don't see grade levels listed for the books we are using. For math we are wrapping up the "standard" 1st grade work and will soon be moving on to "advanced 1st grade/ 2nd grade" work. Our Language Arts program is all 2nd grade materials.
Even with how across the board Sweet Pea is, I consider her 1st grade. I think when most (non-related) people ask small children what grade they are in they are mostly interested in age. It really isn't meaningful to tell people that she is doing certain levels or work and turns people off more then it interests them.
Of course, there are kids who seem to really thrive from not only working at an accelerated pace but also being grade accelerated- I can't speak about those situations because I have no experience there.
For now... we're doing first grade.