The way big oak trees generate is not the same as the way they grow from saplings. This bug has been in the game since the April 20th update of Infdev.
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Actually, if I understand you correctly, I can say with 100% certainty that the pattern of the tree on the left in the pic is how they grow from saplings, and the the pattern of the tree on the right is how they naturally generate.

I do not know enough from your description to say this way or that. And considering that the normal world-generation oak tree planting is (probably still) bugged to begin with, it makes judgements on any other related issue difficult.

May be related to MC-29844
No, it's not, Kumasasa

Is this still a concern in the current Minecraft version? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases. If this has been done, we can reopen the issue.
Keep in mind that the "Resolved"-Status on this ticket just means "Answered", and that we are waiting for further information on whether this issue still exists or not. We will reopen it as soon as the requested information has been delivered.
Ticket resolved as incomplete, because no answer in a reasonable amount of time (1+ year), if it still happens, please update the ticket.

Apparently fixed.
Afaik, there are both intentional and non-intentional differences. See MC-29844 (mentions intentional "temporary" change) and MC-11208 (definitely unintentional one). Also, naturally, each tree is generated (sapling or world creation) with randomness to both size and shape. The description of this issue leaves me scratching head if either of those might be behind this one or not.