My old house in Croydon is a tad larger than my house in Sussex. Both are band C, which makes sense, but the council tax in Croydon is approx £200 less.
I don't think that banding reflects relative current values though. When I moved 30 years ago, both houses were worth the same (well, this one was £250 more, but it's a tiny difference). Zoopla gives the Croydon house a value of £363k-£444k, and I expect it would be at the bottom end of that range because it's now a high crime area (at least 3 murders within a mile of my old house in the last couple of years, and that's just the ones I know about!).
My current house is worth £450k (probably more if I tarted it up a bit), so 20% - 25% more than the one that was worth the same.