For those with Dual Citizenship and both passports the recognised protocol is to enter your home country with your home passport.
Entering the Philippines with British Passport means showing your Naturalisation Certificate and receiving only a BB stamp for 1 year.
The other complication is that the British Embassy will treat you as a Filipino Citizen. So no help there if ever needed.
Likewise entering the UK with your British passport avoids complications and possible delays.
In practice though it really doesn't matter for a short holiday visit to the Paradise Islands