1. See here:
https://www.gov.uk/foreign-travel-advice
You must click to each country and review the "Entry Requirement" for the exact detail. It will indicate if BN(O) Passport holders are exempted or not.
2. No. The major differences in Asia-Pacific are Taiwan, the U.S, and Vietnam.
Taiwan - BN(O) Passport holders are required to secure an online permit for up to 30 days of staying. British Citizen (BC) Passport holders can enter Taiwan visa-free for up to 90 days. A permit is not required.
The U.S. - Both BC and BN(O) Passport holders can enter Guam visa-free under Guam-CNMI Visa Waiver Program. However, only BC Passport holders can enter the rest of the U.S. visa-free under Visa Waiver Program, but not BN(O) Passport holders.
Vietnam - starting from today, BC Passport holders can enter Vietnam visa-free for 15 days. A visa is still required for BN(O) Passport holders.
3. The differences are significant.
HKSAR (and MSAR) Passport shares the same country code with Chinese (Mainland) Passport. As most countries require Chinese (Mainland) Passport holders to apply for a visa, the same country code may create confusions in some countries.
On the other hand, BN(O) Passport has its own country code (GBN). The confusion happened on HKSAR Passport holders will not happen to BN(O) Passport.
Although more countries provide visa-free to HKSAR Passport holders, BN(O) Passport holders can enjoy more ease of travel than using a HKSAR Passport.
2015-07-01 18:35:01 補充:
See some sample countries and you will be able to tell the difference.
Japan:
https://www.gov.uk/foreign-travel-advice/japan/entry-requirements
Taiwan:
https://www.gov.uk/foreign-travel-advice/taiwan/entry-requirements
The U.S.:
https://www.gov.uk/foreign-travel-advice/usa/entry-requirements