Thank you for that Mara Makom.
It is fascinating that all the times that the OH quotes the MB is only in the first and third volume. And according to the sefer you quote (the grandson of Rav Henkin) it should follow that the Halacha only follows the OH in those volumes. What is also strange is that the places that he quotes the CC are random even though he argues on many more places and in about half of the places he acctuly compliments the MB. Also a mute point is that Rav Henkin and Rav Moshe both come from Russia and knew the OH and had no dealing with the CC. On the other hand the Ponavizer Rav who knew both of them held the CC in much higher esteem (see the Bio on the Ponvizer Rav 3 vol). I think the emes is that they are both great sefaim and you cant go wrong going with either one. The CC is a lot more thorough and harder to read (al be he did this on purpose, for a different time).
Also when this grandson of Rav Henkin (in your Mare Makom of Bney Banim writes that the OH is more deep, I have no idea how he knows that or gets that. Some of the Beir Halachas are profound (see in 316 and 261 and others). When he also says we go like the later who had the previous one, see the sefer Machlokes Behalacha that we don’t always say this especially within the same generation (ShachTaz KetzosNesivos GRaGraz….). It also seems that the main Halachic authorities do not agree with his Grandfahter ZT”L (CHazon Ish, Rav Shlomo Zalman, Rav Elyashiv, Rav Moshe held whatever he wanted as you see and as Reb Dovid told me).