We had our back garden astroturfed a few months ago and it's fantastic.
Our garden was a state, with a raised and uneven patio which dropped steeply onto a highly sloped grass area. It was always waterlogged and the drainage was terrible.
If you have the money then plastic is the way to go in my opinion. The best thing about it is that half an hour of sunshine dries it out completely and my kids can roam about without any fear that they'll get filthy or soaking.