In this paper, we investigate the impact of antenna beam pattern models on the beam placement problem in Low Earth Orbit (LEO) satellite networks. Unlike conventional beam placement studies that often rely on a fixed antenna pattern or a predefined half-power beamwidth, this work compares four representative gain models, namely the Bessel $J_1$ model, the combined Bessel $J_1+J_3$ model, the Gaussian model, and a 3GPP-TR 37.842 model. For each antenna pattern, the corresponding half-power angle is obtained and used to construct a user compatibility graph. The beam placement problem is then transformed into a Minimum Clique Cover problem and solved using a graph coloring-based algorithm. Numerical results compare the considered antenna models in terms of the number of active beams, load balancing, statistical channel gain-to-noise ratio (SCGNR), and signal-to-interference-plus-noise ratio (SINR). We analyze the impact of increasing the number of active beams on SINR-based spectral efficiency to explain the importance of carefully controlling the number of active beams. The results show that antenna beam pattern models affect both beam resource usage and link quality, highlighting the need for antenna-pattern-aware beam placement in LEO satellite networks.

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