They are both excellent passports and it is best to apply for both and use whichever is best for each trip.
They both give you the freedom to travel and work around the EU and the Irish one has the advantages of a neutral country that everyone loves. But the British passport also opens a lot of doors with working holiday agreements with many Commonwealth countries.
For a visit to Hong Kong, an Irish passport is best (but 10 years ago the British passport would have been better). Irish citizens are eligible for a working holiday programme that is not available to British citizens. See
http://www.immd.gov.hk/ehtml/hkvisas_10.htm for more info.