They did a piece on Granada (I know :o ) recently comparing the two, and real trees came out way on top in terms of green-ness if you'll allow the pun.
In the UK at least, and I'd imaging similarly here, there's no tree that travels more than 20 miles from it's growing site on average, whereas most artificial trees come from half way round the world in China.
Plastic trees consume large resources in their manufacture while real trees take next to nothing and often are grown on bad land that's no good for anything else. And while growing and re-growing they're doing their thing for the local wildlife too.
In terms of recycling, plastic trees are of course re-used but will eventually have to be dumped, so you're only deferring the usual problems, whereas real trees can be chipped (for free pretty much everywhere) and reused in gardens and so on.