Filipino citizens – old Philippine passport with US visa

I am a permanent resident of Canada, but my Filipino passport expires in January and carries my valid 10-year visa, and I renew it this month. So when my new passport arrives, do I have to reapply for a new US visa with the new passport? Will the customs officer give me trouble traveling with an old passport with a valid visa and my new Philippine passport? Do I need a new I-94 form?