I'm not well informed of the topic and have heard that the Ottoman cannons brought the walls down. I have also heard that someone forgot to close a gate that led inside the city. Which​ one is true?
I'd say that your impression that the city fell "fast" is wrong. Constantinople held on against vastly superior enemy for little less than two months. For more details, check out this thread https://www.reddit.com/r/AskHistorians/comments/45sxv5/why_did_the_1204_siege_of_constantinople_last/ and answers by /u/laklota101
I think both of them are true, it just happened they bombarded on the one place and once the troops were in they put the Ottoman flag, which lowered the moral of the defenders. If you are willing to read a book and be immersed with the details like you are in the siege I recommend this book