Dual nationality, two passports (Manila)

I am looking for some advice please. My 10 month old son, who was born here in the Philippines to a Filipino mother (my wife) qualifies as a British citizen by descent through me. We are planning to get him a Filipino passport in the new year, but I was wondering whether we should also get him a British one too to make international travel, and especially to the UK easier.
Assuming we do that, how do we go about departing from the Philippines, specifically what to show the airline at check-in (I know they are only interested in whether he has a valid passport and permission to enter the country of destination) and the Bureau of Immigration folk, and again when returning (who are more particular, especially here about their citizens traveling and or the stamps etc. in passports.
Thanks
Gary