Yes, the BHP was designed after the
1911. The BHP was only partially designed by JMB, the rest by Saive after JMB died. JMB intended the BHP to be a single stack magazine design, Saive was the one behind the double stack design. Some have said that the BHP design was an improvement over the 1911s design(i.e. linkless barrel , no barrel bushing) .
This is just my opinion, YMMV:
The 1911 is popular in the US, but I don't know if it is the most popular. I believe that it is popular in the US partially because it represents the U.S. . It was designed by an American. It was then Selected into U.S. military service where it served through WWI, WWII, Korea, Vietnam, and other conflicts. A 1911 was carried by our boys during some very trying times.
I have heard some members say that the 1911 is as American as apple pie.
On top of its American heritage and history, the 1911 is very "shootable", lending itself to a wide array of applications.
I don't really have much to say about the BHP because I am not as knowledgeable about it. I own one and I like it a lot. I believe that if you own and enjoy a 1911, you should also own a BHP. They just go together.
I think both are excellent designs, but they are not with out their flaws.