I've taken the liberty to ask a professional rock historian and author to take a gander at the correspondence associated with this thread, and offer a more studied opinion. Further an author who is researching the early days of British progressive rock and written the definitive book on King Crimson, In The Court of King Crimson, i.e. Sid Smith.
This is Sid's succinct response:
When I think of ITCOKC in terms of its influence, it’s nearly always the structure and its unity of presentation that comes to mind as much as the material. It remains a remarkably focussed piece of work; nothing dissipates its impact. Even the circumspect and ephemeral Moonchild improvisation is an essential, coherent aspect of the album’s lucidity. Whilst other bands limber up and develop a sense of their own identity, Crimson seemingly arrived fully-formed. With their very first album, Crimson had refined the various cultural and social influences of the late sixties - the zeitgeist even - into a powerful, unified and original statement.
In doing so, they created a blueprint that others would then adapt to their own needs and dialects; Yes, Genesis, VDGG, Gracious, etc.
After their psychedelic debut, Floyd was a band in flux. Barrett’s departure was cathartic and the upheaval is reflected in the unsettled and slightly muddled follow-up, Saucerful of Secrets. Of course, the live Floyd was a different kettle of fish as the Massed Gadgets suite and the first album of Ummagumma ably demonstrates. As for the studio, it’s not really until Atom Heart Mother that the whole shebang finally starts clicking into place.
Putting aside whether one considers Crimson or Floyd prog (at the time we viewed Floyd as rock and Crimson as something different – prog rock as we understand it today was a term that was still someway off being invented.), I would however concede that Floyd have probably had a greater impact and influence on bands than Crimson given the huge disparity of sales between the two bands.
Best wishes,
Sid