A few days back I created MC-29307 which described how the same seed may give some differences between users. But it was closed because the mods kumasasa and mustek could not replicate the issue. Now, I've found a way to replicate it
1. Create a MC world with a random seed (1.6.2 and modless)
2. Go far from spawn. ie 500 blocks
3. Shut down Minecraft, restart the launcher and load the world again (not sure if this is necessary, but it's what I did)
4. Go further from spawn and look for a jungle (these seem to have most differences)
5. Create some screens and note the coördinates.
6. Do the same on a different PC, different account, of course also 1.6.2 and modless
7. Create screens of the same coordinates. Differences will be visible.
I did it first three times on my own PC only, the locations in the jungle were the same each time, proving the plant growth is not rando.
Afterwards, I did this with two friends of mine, and they had some different versions.
We did extensive research and also found some differences in emerald ore placement in caves! (I'll place two new screenshots of that one) This is rare and me and my friend walked quite a bit through the caves to find such a spot.
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I also did this experiment with some forum users:
http://www.minecraftforum.net/topic/1954587-i-need-people-to-help-me-replicate-a-bug-to-report-it-to-mojang/#entry24069211
One user posted the screens, and yes, there were tree differences in the jungle. He suggested the tree placement was random. But, now look at the last screen I attached,
after the experiment, I repeated it on my own. And: it matched my first result exactly, every tree. So the tree generation isn't random (something the mods confirmed and said: "maybe it changed a few versions back"

Confirmed.
No need to use 2 different PCs or different accounts.
Created two worlds with the seed
MC-29329
one two days ago, one just now.
Coordinates: 1000 / 70 / 11
Duplicate? Which bug is the same? I was glad that this bug finally got confirmed.

In fact, verified the resolution of this ticket. If you save and reload the world while chunks are generated, you'll get different results. See my the screenshot of the third version of the same location.