In general, does it take more processing to render more vertices or many transparent pixels?

I was thinking about modeling ferns as background foliage for a game that would wave as a player passed through it, but then I got to wondering if I should simply paste an image on a rectangular tile of a fern plant that was transparent in all of the space that wasn't occupied by intricate leaves. No matter which method I use, populating a game with hundreds of them is going to take a lot of processing, but which one will dependably take less in most circumstances?

 

It probably all depends on distance to the camera. When closer to the camera, it's probably best to add more detail to the model. That really is generally the case. In the ideal situation, every triangle covers a fixed number of pixels. And different levels of detail is the way to achieve that.