This is a very interesting question!

To answer this, we'll have to not only look at the American side but but in the case of the American-Philippine War, also on the side of the insurgents.

The American-Philippine War.

The American side

The Americans in the Philippines made use of many classical counterinsurgency strategies. Population control in form of resettlement camps to deny the insurgents food, recruits and intelligence were very effective in the Philippines due to the "humane" approach to this. It wasn't in the same vein as the British would later revolutionize during the Malayan Emergency, but the American forces genuinely tried to provide adequate living conditions. While this was happening, an increase in food control was also taking place, denying the insurgents every single food source available by patrolling growing areas and by containing the insurgents in their individual islands instead of allowing them to ship food from one island to another. The policy of attraction was also a good idea; giving medical assistance, building schools and increasing the life quality for the population was a good way to make the population realize that going with the US side of things was better than the rebels.

The good amount of intelligence that became available as the population turned away from the insurgents made it easier to hunt down and kill insurgency leaders and ambush local guerrillas. The use of assassination to kill insurgency infrastructure in villages was also carried out, something which was also used during the Vietnam War (Operation Phoenix). There was also a policy of reconciliation carried out, allowing insurgents to turn themselves in and become productive members of society. Indigenous soldiers were embedded into US infantry units often fighting with just rifles. The use of ethnic forces in active service was a way of making them feel part of the overall goal and build up trust. Another brilliant aspect was letting US commanders on the field, from the ordinary NCO to the general, to adjust their tactics and strategies to the realities in the field which in turn produced great successes - and terrible crimes.

The warfare carried out by the Americans in the Philippines was brutal. The amount of civilians who died overshadows the idea of an American victory in the Philippines since you do not win counterinsurgencies through the killing of civilians, but by gaining their trust and support. Massacres, local policies of destruction and deaths of civilians in garrisoned towns were all crimes that the US were responsible of. It was the combined factors of a few good policies (mentioned above), primitive counterinsurgency tactics more drawn from colonial war than we can call modern counterinsurgency as well as facing an at times incompetent and marginalized insurgency that committed as many mistakes as the US.

The Filipino side

The guerilla leadership were from the higher classes of Philippine society (Ilustrados) and thus were disconnected from the reality of the majority of Filipinos. Even the same class they belonged to kept a distance and with limited support since the movement was essentially limited to Tagalogs, they weren't getting anywhere. Some of the population even feared the insurgents more than they did the Americans. The crimes committed by the insurgency completely overshadows that of the Americans yet is quite often ignored. The crimes occured more often and were not late in setting fire to entire hamlets to punish or prevent cooperation with US forces. After the creation of the indigenous Federal Party, a pro-US political party that was meant to exist as an alternative to the insurgents, the guerrillas did not hesitate in threatening to execute all male inhibitants of villages that were even remotely positive towards the US. ^1

The guerrillas also had the disadvantage of not being supported from the outside, being effectively isolated to their own country and were very badly armed from US efforts of collecting and buying rifles around the country. Since the tide was turning against the insurgents in late 1900, an event that would shatter the insurgency within a year occured: the capture of its leader through an amazing intelligence coup.

In 1901, the capture of an enemy courier led to the acquire of a letter from Emilio Aguinaldo, the commander of the Philippine insurgents. The letter was to Aguinaldo's cousin and was a request for reinforcements to his headquarters (and hiding place) in the mountains of Palan. After further investigation (and interrogation of the courier), it was decided to make up a plan to capture him.

The plan was as follows: 80 Macebe scouts (these were Filipinos from the town of Macebe which traditionally served Spain) who could speak Tagalog would be dressed up as insurgents together with 4 Tagalog loyal to the Americans who would dress up as officers. These men would then enter the hideout together with 5 American "prisoners". One of the prisoners would be none other than Brigadier General Fred Funston himself. Two letters would also be sent to Aguinaldo, complete with official stationary from an insurgent base and forged signature, to make the party with prisoners seem less suspicious.

After a grueling 100-mile trek and the crossing of the Palan River, two of the disguised Tagalog officers entered the base while awaiting the Macebe scouts to show up (since they had to cross the river). Aguinaldo had taken the bait and greeted them with a complete honor guard. When the Macebe scouts arrived, they took position as to prepare to salute Aguinaldo, only to open fire at the guards at the hideout when a signal was called out. Startled and surprised, the Tagalog officers quickly seized Aguinaldo and together with the five American "prisoners", escaped.

Aguinaldo was taken to Manila to meet with General MacArthur and a month later took an oath of allegiance to the United States together with a proclamation to all the insurgents to lay down arms. Despite the loss of the highest ranking commander that the Filipinos had, the war continued on for another year.

The Vietnam War

While I would rather redirect you to this post I've written on counterinsurgency during the Vietnam War, there are some points I need to make. The US was simply not prepared for counterinsurgency in Vietnam and treated it as a conventional conflict. Right from the start, any counterinsurgency strategy was thrown out and replaced by conventional strategies which simply had no basis in reality. The draft turned in young men who were not even prepared for a counterinsurgency war and whose cultural understanding of the South Vietnamese was next to zero. The US strategy in the Vietnam War was so catastrophical that it was one of the main reasons to why US soldiers turned away from the war and led to demoralization. The political aspect of this just simply can not be ignored. While there was a widespread protest against the Philippine War amongst the intellectual elite, it never really reached out to the voting masses - unlike the Vietnam War. Another reason was the fact that the VC, which was essentially created and controlled from North Vietnam, was heavily invested by an outside power which in turn was supported by China and the Soviet Union with everything they needed. They were not left out in the cold, unlike the Filipinos.

^1 Pg. 45 Counterinsurgency in the Philippines 1898-1954 by Prof. Anthony James Joes in Counterinsurgency in Modern Warfare (ed. Marston & Malkasian).

The Philippine guerillas were isolated by the US Navy and received little, if any support from a third party. The Viet Cong received a lot of help from North Vietnam. North Vietnam was strongly supported by the Soviet Union. The US Army suppressing the Philippines was a volunteer army and fairly small. The US Army in South Vietnam was a larger army, of conscripts. The draft was extremely unpopular during the Vietnam war and it galvanized the opponents of that war to a much larger degree than those who were opposed to American Imperialism in the Philippines were able to achieve. The war in Vietnam was televised and it was a major topic of discussion between 1965 and 1973. Newspapers did cover the Philippine insurrection, but it did not have the critical mass that the Vietnam war had. Source "A Country Made by War, the Military History of the United States" by Geoffrey Perret.