My cat eats grass because she likes a salad before dinner, I think.
Anyway, I know she prefers real grass (it's maybe crabgrass, I think? It crops up unasked-for in my balcony plant pots) over "cat grass" (oat/wheat/rye from seeds) growing in the kitchen window, but will eat both.
And it doesn't make her vomit, it just helps her poop.