What’s the safest way to transfer money from the Philippines to the US (wire, online services, or banks)?

Bank transfers are usually the safest. In your reference you cited, wire-transfer, online or through bank.

All these are essentially the same. The only difference is, if the service is being provided by the bank itself (like BDO, etc.) or by an non-banking financial institution (like Xoom or TransferMate, etc.).