No, vegetarian athletes do not perform better or worse compared to omnivorous athletes . Studies have found that vegan, vegetarian, and omnivorous runners demonstrate comparable exercise capacity, suggesting that all three diets can be suitable for athletes with careful planning .
Although vegetarian diets aren’t necessarily superior for sports performance, vegetarian diets may have longer health benefits for athletes including reducing oxidative stress and regulating the anti-inflammatory response . Plant-based diets may also be beneficial for improving cardiovascular markers, body composition, glycogen storage, and blood pressure .
That said, vegetarian athletes may be at increased risk of micronutrient deficiencies including omega-3, iron, zinc, calcium, and vitamin B12, and careful planning is required to ensure adequate intake of these nutrients and avoid decrements in performance . For more information on plant-based diets for athletes see this article.
 Devrim-Lanpir, A., Hill, L., & Knechtle, B. (2021). Efficacy of Popular Diets Applied by Endurance Athletes on Sports Performance: Beneficial or Detrimental? A Narrative Review. Nutrients, 13(2), 491. https://doi.org/10.3390/nu13020491
 Nebl, J., Haufe, S., Eigendorf, J., Wasserfurth, P., Tegtbur, U., & Hahn, A. (2019). Exercise capacity of vegan, lacto-ovo-vegetarian and omnivorous recreational runners. Journal of the International Society of Sports Nutrition, 16(1), 23. https://doi.org/10.1186/s12970-019-0289-4
 Barnard, N. D., Goldman, D. M., Loomis, J. F., Kahleova, H., Levin, S. M., Neabore, S., & Batts, T. C. (2019). Plant-Based Diets for Cardiovascular Safety and Performance in Endurance Sports. Nutrients, 11(1), 130. https://doi.org/10.3390/nu11010130