catkan has answered pretty well.
Catholic Church 天主教會 is actually more united to the Vatican and the Pope, but the Anglican Church 聖公會 is more of functioning region by region.
The Catholic Church is more modern in its liturgies, while the Angelican Church is more classicly Latin. There are more hymns (church songs) translated into diff languages in Catholic C. and most hymns in Anglican C. are in Latin.
One special thing about 聖公會 is that it is quite British, and there is even one national flag of the UK in st John's Cathedral in HK.
As for the Catholic CHurch, it is the church that is directly set up by Jesus Christ, and through the Vatican this church has many different instructions for churches in different countries and the instructions are carried out based on cultures of different regions. But all churches act based on the same principals.
一个大分别是,圣公会的司铎(牧师)结婚,收人工,司铎一分职业;天主教的司铎单身,在教会生活服务,不受人工,是一奉献生活。
Catholic C is a warm church while as serious as it is when it is necessary. In my opinion, the good thing about Catholic C is that it is more open to different religions while it sticks to its own doctrines; and it is generally more united and peaceful.
Im very sorry as I do not know very much about the Anglican C.
天主教徒谨守二千年来的原则:爱天主,爱人(especially those in need); 为更多人的灵魂的得救而把福音传开.
彌撒聖祭以粵語進行,但有五分之三的堂區也使用英語,有時也採用菲律賓語。香港教區設有本身的行政組織,並與教宗及世界各地教區保持密切聯繫。香港教區與世界各地其他天主教區一樣,均採用同樣的《聖經》、教義、崇拜儀式和架構組織。
除了傳道外,香港教區也十分關注市民的福利。在教育方面,本港有天主教學校和幼稚園297所,就讀學生約24萬人,辦學工作由天主教教育事務處協助進行。教會開辦的醫療和社會服務機構計有醫院六家、診所13家、社會及家庭服務中心39所、宿舍18所、安老院13所、康復服務中心20所,以及自助會社和協會多個。
香港明愛是統籌天主教香港教區各項社會福利服務的組織。香港教區提供的各項服務,普羅大眾均可享用!受惠人士當中,多至九成半並非天主教徒。
香港教區除每星期出版中英文《公教報》外,還攝製文化和教育節目,供電視台播映,並以數碼影像光碟方式派發。教區參與媒體的事務,一般由香港天主教社會傳播處統籌。
Maybe these websites would be useful for you:
聖公會:
http://www.stjohnscathedral.org.hk/chi/home.html
http://www1.hkskh.org/index_ch.php
天主教:
www.cathedral.catholic.org.hk/
http://www.catholic.org.hk/v2/b5/index.html