Randy Sandke uses the word "nuances." Dave Jellema notes "the three-beat scoop, the dip, the bend up to the next note in the last beat of the fourth bar..." Both of these comments allude to the subtle "jazzing" (for lack of a better phrase) that Bix injected into his cornet playing.
Jazz phrasing and articulation on wind instruments largely imitates the tone and inflection and natural rhythms of the English-speaking voice. This is what sets jazz apart from the European classical music tradition. One of the biggest "give-aways" that a musician playing jazz is not experienced in the idiom is a poor or sloppy use of jazz phrasing and articulation.
This is what sets Secrest and Bix apart. First, let's give Secrest his due. I love his playing. He definitely improved with age, and by the time he cut "Smarty" with Bing Crosby (1937) he had developed a wonderful, unique style and his cornet playing was superb. Even during his apprenticeship with Bix, Secrest played well, certainly a cut above most cornet soloists with the dance bands of the day. But at the time Secrest was with Paul Whiteman, he still had not fully developed the use of those little jazz "nuances" that made Bix's playing extraordinary. Secrest pulls them off some of the time; other times he sounds like he is working really hard but still not getting it. Listen to his muted solo on "Nobody's Sweetheart." Secrest sounds strained, and the harder he works, the more his intonation suffers. But again let's put things in perspective. When Secrest recorded "Nobody's Sweetheart" he was barely twenty two years old. He was just shy of his 30th birthday when he recorded "Smarty."
There were other cornetists from the same period who also mastered those "nuances" pretty well. Jimmy McPartland did, but still not quite on Bix's level. Red Nichols did. His technical skill as a cornetist was extraordinary, but he played on the beat rather than around it (probably an artifact of his musical training in the military band style) so his playing is still plagued with a kind of stiffness.
But with regard to those "nuances," Bix (in my humble opinion) is in a class by himself. Those little things, the bends, the scoops, the dips, the notes held just a fraction over the start of the next beat -- and all with perfect intonation! -- that is what defines the kind of cornet solo that only Bix could play.
Like Randy Sandke, I hear those things in the solo on "Waiting At The End Of The Road." Or to put it another way, that solo has always given me "the Bix vibe". I've never doubted for a minute that the soloist is Bix.