I've already gone over the Pokémon that changed tiers solely because of the new weighting system, but I just wanted to push it a step further and compare some Pokémon that don't change tiers, but whose ranking varies wildly.
For reference purposes, here are the stats with the old weighting method and the new one.
So many big changes. Bisharp goes from #21 to #5, Landorus-T from #20 to #7, Keldeo from #39 to #10, Chansey from #40 to #23 (in fact it's even more popular than Blissey at higher levels of play), Landorus-I from #58 to #25... There are also several Pokémon who took a nasty tumble, especially Greninja (#5 to #21), Togekiss (#26 to #41) and Volcarona (#35 to #55).
On another subject, last month I wondered whether Mega Lucario's ban would mean the disappearance of its base form from OU, and the numbers I had back then gave us the right idea: vanilla Lucario just doesn't cut it anymore, at #82. Was Gamefreak targeting it for a mega evolution amazing foresight or sheer dumb luck? Either way, I think we can agree Adaptability was freaking overkill. Heck, there's no need for a super godly ability for previously bad Pokémon to rise to fame - Mega Manectric is currently making Jolteon quite obsolete armed with just the standard issue Intimidate, to such an extent that it should enter OU very soon. Of course it makes an amazing VoltTurn core with Landorus-T, who also has Intimidate, but my point is, even the megas that don't have terrifyingly good abilities are making a name for themselves.