My understanding was that the two-spool turbofan Spey (vs the single spool turbojet J79) produced more thrust at low speed and low altitude for improved take off from the smallish RN carriers, and provided more bleed air for the Phantom's boundary layer control system for improved landing speed onto the smaller carriers. But the higher airflow required increasing the intake area 20% and a pretty drastic redesign of the aft fuselage. These combined to slightly increase form drag (which was more than overcome by the increased thrust) and significantly increased wave drag while reducing intake recovery at high mach (over 1.6) which resulted in a lower top speed. But the Spey's biggest contribution was significantly improved fuel consumption. If memory serves about 15% improvement in combat radius and nearly 20% in ferry range, pretty impressive considering that form drag had gone up.