It is a TON different, and that's ultimately why I'm against it. This would effect the game in many ways that were pretty unpredictable, but I'm going to take a stab at a one prediction (and some ramifications) that I think is likely:
TL;DR - Duo lane mid, mages suck now
With dragon in the middle, the marksman will be there, too. I think it's likely the support moves with them, given that supports want to roam anyway (and we'll see more of that). This will make mages suck because there's no safe lane for them anymore.
Many people started playing this game too late to understand the current macro-meta. Let me explain (for other's benefit if OP already knows):
Mid lane is the shortest lane, and therefore the safest from ganks. Marksmen used to be mid lane because of this, but by swapping bot lane and letting them lane with a support, you actually create an additional safe lane, essentially. Mid lane is short for immobile mages, and bot lane has the protection of a support.
Top lane remains the most dangerous lane, which is why fighters and tanks are the "meta" up there. They have a chance of surviving long enough to get back to tower in the event of a gank, even though they are in a long lane alone.
If you swap dragon and baron to mid, what you do is force the objective control class (marksmen) into the mid lane and mages have no safe lane to use. I think we'd see a pretty drastic reduction in their efficacy as a result.
Even if that's wrong, the potential to flip critical game systems on their head in this fashion is simply too high imo. It's a risk that doesn't add enough to the game to justify taking it in the first place. A solution to a non-existent problem, if you will. The outer lanes already have reduced influence compared to mid in a truly symmetric game because mid is more central, simple as that.
If you were making a new MOBA, maybe this would be an interesting way to distinguish yourself from the competition, but I don't think there's even the potential for a big enough payout to risk it with League.