Your comment about commonalities brings to mind the fact that, though the music itself might be different, the reaction of the British press to the ODJB in 1919-1920, during their London sojourn, was very similar to the reaction of the British press to punk rock in 1976-1977 (i.e. a mixture of revulsion, haughty disdain and inordinate fascination!).
As far as popular music lineage goes, basically it's Ragtime and Spirituals to Jazz & Blues to R&B to Rock & Roll to Pop. A vast oversimplification of course, but that's the basic chronological progression of the genres! The connection to Bix does seem rather tenuous, but I don't see why it's an insult to him, as Joe Mosbrook proclaims!
For a more nuanced assessment of the influence that Bix has had on popular music since his death, one needs to refer to The Observer newspaper of August 2nd, 1981. In an article entitled "The Great Bix Beiderbecke", the British jazz critic Dave Gelly (now OBE) states:-
"Unlike Louis Armstrong, almost exactly his contemporary, Bix had behind him not the African heritage of the blues, but the European musical tradition brought to America by his German ancestors. His unique contribution to jazz history, apart from his own genius, was to establish a style in which European notions of pitch and tone fitted happily into the Afro-American idiom. From Bix to Benny Goodman to Stan Getz, the development of that style can be discerned quite clearly.
It can be found, too, in the line of white popular singers which descends from Bing Crosby. Beiderbecke and Crosby were both members of the Paul Whiteman orchestra in the late Twenties and Bing often told, in later years, of how he had modelled his phrasing on Bix. The coincidence is suspiciously neat, but another new album from that period, 'Bix 'n' Bing' (ASV Living Era AJA 5005) illustrates the uncanny similarity between the two.
The Beiderbecke-Crosby connection is, therefore, directly responsible for that whole fertile tract of popular music - half jazz, half sentimental ballad - which we associate with artists like Frank Sinatra. More than half a century after they were made, the records prove the case conclusively".
I think Mr Gelly slightly over-eggs his pudding here, but when one considers that a number of today's pop singers publically promulgate the notion that they have been influenced by the likes of Frank Sinatra (including Adele - hence her name being mentioned in the title), the comment that Brendan Wolfe makes seems to carry some weight, if a little unevenly distributed!