Also as per ur comment that the CC felt himself secondary to Rav Chaim Ozer that is not really a shocker. I think he felt himself secondary to everyone as he writes himself in Shmiras Halashon and many other places (meaning that if u learned alot now you are alot more responsible) and the CC main Mida as said over by his Talmidim (see Meir Einey Yisrael vol 1) was Anavah. The best way to find out who was greater would b to see how Rav Chaim ozer viewed him and when they were together who was the Machriafirst… But I think if you asked them both they would say the other is (as you see in the story about the theater which is quoted both in Meir Einey Yisrael with two versions and also in the Artscroll bio).
PS There is a famous zug that’s said over from Rav Shach that the CC quotes Rav Meir Simcha once because of the Masseh in Velozin. See the Meir Einey Yisrael why that Maseh is immposible to b true (one reason is that in the volume where he quotes Rav meir Simcha it was printed before the maseh happened). Im just writing this to show that just because someone said something without documented sources its validity is…