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Many people would claim that either one of the mentioned 3 concepts is more superior than the other to improve your core strength. But before I comment further about the claim, let me briefly describe each concept.
Yoga- According to the NHS website, Yoga is an ancient form of exercise that focuses on strength, flexibility and breathing to boost physical and mental wellbeing. The main components of yoga are postures (a series of movements designed to increase strength and flexibility) and breathing.
Pilates- U.S.P.A states that pilates is not just an exercise; It is a series of very precise, controlled movements that fully engage the body and mind. These movements are performed on exercise apparatus which was designed to support and guide the body through its ultimate transformation. Programs are tapered uniquely to each individual and their needs through the watchful and experienced eye of a pilates instructor.
Core Stability Exercise- To allow movement, carry loads and protect the spinal cord and nerve roots “stability” is required. Stability is provided in a co-ordinated manner by the active (eg muscles), passive (eg lumbar spine) and control (eg neurological systems). Traditionally, core stability has been referred to the active component to the stabilising system including deep/local muscles that provide segmental stability (eg transversus abdominis, lumbar multifidus). Different proponents have advocated different types of core stability exercises ranging from the abdominal drawing in maneuver to “plank” type exercises.
My take on this is:
Each concept has its own principles and overlaps might exist but they all promote core strength.
Yoga and Pilates might attract more people because it is sounds different and it offers a variety of exercise with different equipments or tools.
PTs would normally prescribe core stability exercises but the exercises can be quite boring.
All three concepts are equally good to strengthen your core.
Bottom line
Personally as a PT, I do not show favourability to any of the three concepts in improving core strength. If we have to factor in cost effectiveness then I would choose core stability exercises to strengthen the core. Core stability exercises can be done without equipments or constant supervision. The best part is it is relatively cheap.