Non diffracting (ND) beams are often cited as a promising solution to mitigate blockage in millimeter wave (mmWave) systems. However, a quantitative answer to the fundamental question, under what specific conditions do ND beams actually outperform conventional pencil beams, has remained elusive, especially in the emerging context of near-field communications. This paper provides the first systematic answer by mapping the performance advantage regimes of ND beams for blockage-resilient near-field links. We propose a unified holographic generator that synthesizes various structured beams (e.g., Bessel, Mathieu) under the physical constraints of a planar phased array, ensuring a fair comparison against a boresight baseline with identical EIRP and aperture. Through extensive, unbiased Monte Carlo simulations, we construct advantage regime maps that delineate the specific regions where ND beams offer a tangible link-level gain. Our key finding is that the advantage of ND beams is a powerful but conditional near field phenomenon. While offering a positive average gain, its performance is highly variable, with a 60-70% probability of outperforming the baseline in its optimal range. Crucially, this performance is strongly modulated by the obstacle's geometry, revealing a significant weakness against large blockers. These findings provide not just a practical roadmap for judiciously employing ND beams but also a clear motivation for future work in environment-aware, adaptively shaped structured beams.