AbstractIn the Palaearctic steppe zone, overgrazing was identified as one of the key drivers of declining grassland biodiversity, which underlines the necessity of the functional evaluation of increased grazing pressure on grassland vegetation. We tested the following hypotheses: (a) The effect of grazing intensity on species and functional diversity is strongly dependent on grassland type. (b) The magnitude of diet selectivity of grazers decreases with increasing grazing intensity. (c) Increasing grazing intensity increases evenness and functional evenness of the subjected grasslands. We analyzed vegetation patterns in four types of grasslands (Dry alkali short‐grass steppes, Dry loess steppes, Non‐alkali wet and Alkali wet grasslands) along an intensity gradient of beef cattle grazing at 73 sites in Hungary. Species richness, Shannon diversity, evenness, and four leaf traits were analyzed. We calculated community‐weighted means for each single trait, and multi‐trait functional richness, functional evenness, and divergence for all leaf traits. All species and functional diversity metrics were significantly affected by the grassland type, except leaf dry matter content. The effect of interaction between grazing intensity and grassland type was also significant for functional richness, functional evenness, community‐weighted means of leaf area, and for species richness and evenness. An upward trend of specific leaf area was detected in all grasslands with the highest scores for the overgrazed sites, but the change was also grassland type dependent. The detected trend suggests that with increased intensity the overall selectivity of grazing decreased. We found that evenness was affected but functional evenness was not affected by grazing intensity. Functional evenness scores were more related to the grassland type than to changes in grazing intensity, and displayed a high variability. We stress that one‐size‐fits‐all strategies cannot be recommended and actions should be fine‐tuned at least at the level of grassland type.