Lets suppose.

[2D]

That there are three identical earths where the only variable is what life is on them. One with humans, animals, and plant life. One with only animals (no humans). And one with only plant life. Which do you suppose would fare better in the long term?

[mrmcdonaldduck]

plants.

[Kaleidoscope Eyes]

First planet: Well, assuming that it is basically identical to this planet, I think we can also assume that it would fare about how the planet is doing now.

Second planet: Only non-human animals. Would it have any sort of plant life? If not, and if these animals are the same ones we have now, then the animals would die out pretty fast, what with having no plants to recycle carbon dioxide back into breathable oxygen. Gradually, all species would asphyxiate and die out.

Third planet: At first glance it seems like this one might do just fine. From to a purely scientific view, life on our planet was originally all single-celled organisms. Then plants came along, and eventually things got to where we had aquatic creatures who eventually came out onto dry land, you know the drill. If we could assume that this type of evolution would not occur on this planet, beyond plants and any organisms that you might not consider to be "animals" then the only issue would be certain plants slowly becoming more overgrown and pushing other plants out of existence. With no animals to need those plants for survival, though, that shouldn't really affect things much.

Would insects and other bugs exist on this planet? Or would it be strictly plants?
Without bugs, the planet would slowly collapse in a similar fashion to the second one. Bees, for example, are necessary to pollinate certain plants. I've seen the consequences of bee shortages here in California, where we grow a lot of citrus fruits. Those plants need the bees in order to grow to their full potential and stay their happiest. Without bees at all, a lo of plants wouldn't do very well and would dwindle, potentially to extinction over a long enough time. Certain bugs are necessary to other plants as well. The insect lives in/on the plant, or eats it, and in the process actually keeps the plant healthy.

Once we assume that we even have the insects, though, we run into another problem: With no fish or birds or anteaters or anything to curb the insect population, the bugs would go wild and we would see the extinction of many plant species. Some would evolve to become more pest-resistant, some wouldn't. I don't think all would necessarily die out, but after a few million years who knows?

My conclusion: Yes, humans are pretty damn destructive, but we are working on that and we can prevent the problems we've caused from getting tooooo much worse, and even start to reverse some of them. The planet might be fine without us but still having everything else, I don't know, but having just animals or just plants probably wouldn't last in the long run. Even a single species being extinct can have some pretty drastic effects on the ecosystem, imagine the effect of having thousands upon thousands just never showing up?

The other option, of course is that everything evolves in such a way that they can survive on what IS available to them, which would put the animal planet and the plant planet on pretty equal footing... but then the planet wouldn't be identical to ours at all except for things like climate and geographical features, and things like that.

[INFERNO]

That there are three identical earths where the only variable is what life is on them. One with humans, animals, and plant life. One with only animals (no humans). And one with only plant life. Which do you suppose would fare better in the long term?

I'm assuming that when you say animals, you're including bacteria, fungi, insects, fish, birds, etc... . I'll go in order of what is the easiest to explain. I'm also going to assume that these organisms are plopped onto the planet and don't evolve onto the planet. If we consider they do evolve then the situation for all three planets becomes much more complex, especially for the second and third planets.

The second planet is pretty much doomed because if they resemble today's non-humans, then we need oxygen. Since no plants are around, this planet is pretty much doomed from the start.

The third planet is also doomed because numerous plants would fail at reproducing new generations as they depend on non-plant organisms, which aren't present. Also, there's the problem with over-growth. Think about it in terms of a beaver, it's teeth continuously grow and it needs to maintain their length otherwise it dies by its own means. Plants would have nothing to regulate their growth and combined with no organisms to help plants reproduce, it's pretty much screwed. I do think though that it wouldn't be as doomed as the second planet is though because chances are the plants can still get nutrients and everything else they need and some plants can reproduce without non-plant organisms. These ones may be the ones that survive. But there comes the problem here: the other plants will use up many nutrients before they die and without non-plant organisms to help regulate this, the plants are screwed.

The first planet I view as the "control planet" because it's exactly like ours is and so there's no need to conceptualize how it would be.

Alternatively, if you mean "animals" to not include insects, bacteria, fungi, fishes, etc..., then yes, the first and second planet are doomed. The third planet doesn't have any of these to begin with so this issue doesn't apply to it anyways but it is doomed regardless.