We also have the grout carbide wheels for the dremel but the dremel is too loud of a tool for me (especially when working @ night), and it also creates a lot more dust. I find that buying several sets of the grout grabber goes a long way. Just have several of them w/ you, in case one breaks, and or wears out.
You can do a 200 sqft room in under a hour w/ it, but if you need to remove/reset furniture than it'll take a little longer.
I recommend having a quart bottle filled w/ water, and fine misting the areas you're about to remove the grout from, this keeps the grout dust from getting too airborne (similar to the video above), if you don't fine mist it, it'll create some dust, but nothing close to the dremel.
Xactimate pays $2.50/sqft, than I add min 2 hours content r/r @ $55/hour, w/ optional tile cleaning/sealing few days later. It depends on job/distance.
Most tile guys charge $4-7/sqft when doing regrouting.