In many cases, just marginally better.
Lets say a traditional remittance transfer is 3% between US and Philippines, so for the $1,000 you are sending, the fees is $30.
On the Bitcoin front, this might be about 0.75% to 1.0% at best. So you are paying $7.50 to $10 for the transfer.
Great savings? Perhaps!
You need to find an exchange in the US to buy bitcoins from, and likewise find a bitcoin exchange in Manila to sell to and cash out. Both exchanges will levy a fees.
Depending on how quickly you can have the coins transported from US to PH (assuming no wild fluctuations there), and then sell and cash out to your bank account, the savings will be there, but only on a small, individual basis.
Remittances are usually small value (compared to business payments), averaging between $250 to $5,000. Reality is, the margins on remittances are quite narrow. Competing on price and expecting a large savings is only possible if the average transaction value is higher.
So if you send say $5,000 then the savings over the year can be substantial. However, if you occasionally send money, the savings might not be super efficient.
The existing players in the remittance industry are always facing a downward pressure to reduce price. However, if you were to treat this operation from a commercial point of view, the numbers a marginally better (because of licensing and compliance costs).