lol actually it seems you have little idea about air warfare.
Do you know when defending a country's air corridors which is preferred way?
It was always fighter vs fighter it never was SAM vs fighters.
There is no 'preferred' method in air defense. The reason is because it depends on what the enemy want and his methods of achieving his goals.
If the goal is to support a ground invasion, then the attack mode will be strike aircrafts, meaning aircrafts that deliver weapons against ground targets or to say 'attack from the third dimension'. Assume for now the defender have no air force of its own. In this case, air power will be strictly of strike fighters, close air support, and strategic bombers. For the defender, SAM will be the only defense method. But the key is this: Fighters do not win wars, strike aircrafts do.
Fighters are air-air weapons, but it is always the ground victories by the army that win wars, so from that perspective, the strike fighter, which includes close air support (CAS), is a more valuable component in the war.
Let us for a moment go to the absurd. Side A have only air superiority fighters. Side B have no air superiority fighters, but plenty of strike, CAS, and bombers. Side B will win the war. Even if Side A have as much aircrafts as Side B, air combat is so dynamic and there are so many possible ways to enter an area, Side B will be able to do enough damages to A's ground forces that B's army will be able defeat A's army.
Actually, the above scenario is not that absurd: The Vietnam War. Back in the Vietnam War, the North Vietnamese have no air force to do any statistically significant damage to US air power. A couple dozen MIG-21s and that was all. US air power absolutely dominated North Vietnamese airspace. North Vietnamese air defense composed strictly of surface to air missiles (SAM) and AA guns. The word 'strictly' is no exaggeration. Because there were so few MIG-21s, North Vietnamese ground defense forces never relied on the MIGs as a vital component of the war. The MIGs were accessories to the war, never instrumental. North Viet Nam was never invaded was because of political reasons, not military reasons.
The problem here is that people falsely perceives air defense to be persistent, meaning that you can win a war strictly by being on the defensive posture. The best way for a ground force, or a fixed and important land feature such as a building or the President or an ammo depot, to survive is to go after the capability that can attack that ground army or building or the President or the ammo depot. The air defense component is supposed to be temporary, meaning to fight just long enough to survive while an offensive counter air campaign is conducted against the enemy airfields that sent those attackers.
So which is better, an air defense that uses only air-air fighters, only SAMs, or the appropriate combinations of both ?
If the attackers send 100 bombers, and if the defender have only air-air fighters, then the defender better have 100 fighters, because if the attacker is determined enough, he will endure losses of those 100 bombers and enough of his force will survive to drop bombs on the defender. We saw this back in WW II when the defender, Germans or Japanese, could not field enough Messerschmitts or Zeros against Allied bombers who had no escorts. Many bombers were shot down but many made it past the fighter gauntlet to drop their bombs.
In a manner of speaking, surface to air missiles (SAM) are improved anti-aircraft bullets. The problem is that 'improved' does not equal to perfection. If each missile have a 50% chance of success, it does not mean the defender can send up 200 missiles and those 100 bombers will be destroyed. Each missile still have only 50% chance of hitting any bomber, so two missiles going after one bomber can still miss. Back in WW II, it took literally hundreds and even thousands of various AA shells just to hit one bomber.
If the attacker is overwhelming like the Allied air power in WW II or US air power in the Vietnam War, even a combination of fighters and SAM will
NOT be any effective air defense. Stalin once said: Quantity have a quality of its own.
A surface to air missile (SAM) is much less expensive than a manned jet fighter but that is not the reason why the SAM is so vital a component in war. History have already shown us what happened when there is one air defense method but not the other: The attacker got thru.
The manned fighter is better than the SAM in the sense that the fighter can pursue its opponent, meaning if the strike fighter or bomber drops altitude, the fighter can follow or even anticipate. Pilots can plan ambushes, SAMs cannot. Even if the attacker believe he may survive SAM batteries, the knowledge that he will face this weapon will compel him to make changes to his plan. He may try to enter the area at a different altitude, or chose to fly thru mountains, or skim the surface of the sea, or fly at higher altitude. The smart defender will place his air-air fighter at points that can intercept the attackers, killed some, hope that the SAM batteries can kill a few more if not all, and whatever attacker remain will not do as much damages as originally feared.
Air defense is not a simple subject. Even placements of SAM batteries require days of planning. Since the enemy must support
HIS ground objectives in the hope to win the war, terrain dictate how he will enter the fight, even if he is attacking from the 3rd dimension. The nature of the defensive weapon affects the attacker's movements. The wise defender, if he has at his disposal both SAM and fighter, will use the nature of one weapon to produce predictable responses from the attacker, and ambush said responses with the other weapon. For example, the defender can use his fighters to force the attackers to a lower altitude where his SAM can ambush the descending attackers, and remember, the attacker is trying to support/achieve his ground objectives.
But...If the defender does not have both, best he can do is hope he can survive.