It seems you are incapable of understanding how those attacks actually inflict damage . Barjung gun deals physical damage .
Flame dragon purpose is to melt things , not only its common sense but its confirmed in manga 3 times in chapter 1048 :
- Kaido saying to Luffy this when he used flame dragon "The hero of this country was burned to death"
-Kaido saying to Luffy before clashing with fist " That giant fist of yours will not come down on me ,it will melt into nothing first "
- Luffy saying to Kaido before clashing " I am not melting , the old man taught me how to do that without touching ".
Luffy made it clear he would hit him without making contact which would negate all purpose of Kaido dragon so in order to prevent that Kaido had to use his own haki to overpower Luffys haki and once hes done that he will melt him.
This is further confirmed by fact when Luffy introduced Barjung gun haki lightings were all over it ( telling us his attack is infused with it ), while when Kaido used flame dragon no haki was shown around it at all , and no haki was seen in couple panels too . In fact first time haki was shown coming from flame dragon was during clash and only after Luffy words of how he will punch him without making contact thanks to haki.
Knowing how flame dragon is meant to deal damage its clear it has nothing on PS.