grass, hay or straw?

Freshly mown grass is nitrogen-rich and shouldn't be spread as a mulch over plants, since it will suck up the nutrients from the plant. How about dried grass? 

I've spread some dried grass clippings to cover up the soil around the radish, kale, and broccoli, but as an experiment, I've also covered parts of it with the dried conifer leaf mulch to see if that works better. 

I'm worried that the seeds in the grass clippings will actually sprout and cause a grass invasion, though. That would be a pain -- what's the adage that's in all gardening books: one year's seeds, seven years' weeds.