Overfinch are the ‘original’ RR modifiers. Their work could be quite garish (more often than not IMO) but also quite cool (things like gun racks, minibars etc). They also did a lot for the power. I think they were also approved by RR.
Kahn aimed more at the footballer end of the style spectrum. I don’t know what they do in terms of power.
I believe Kahn now own Overfinch as they have been a lot more successful in recent years.
Interestingly I have noticed that Brabus now don’t seem to be able to add much power to Mercs like they used to as Mercedes now tune their cars very well. Brabus just seem to spend all the money on over the top styling now to the point they look embarrassing.