What progress is synced between platforms when I log in with my Origin account?

Solution 1:

Speaking from a combination of personal experience and media articles your Speed Points are tracked between all platforms.

I played extensively on the Xbox 360 and when I later received the game for PC my Speed Points were still in the millions despite being starting a "new game". From the article linked above, this should have also applied to Sony and Nintendo devices too.

Because the multiplayer in NFS MW:2012 works based off your Speed Points rather than in-game accolades you have your car unlocks too. I can't attest to cosmetic upgrades or vehicle upgrades for your unlocked cars in multiplayer, but I suspect those would transfer as well.

In single player no progress transferred for me, with one exception. All of my races were not yet completed and all billboards were still unsmashed, I still had to go out and find cars that I wanted to drive. All of this was just like I had started a new game except I had a ridiculous number of Speed Points already accrued. This meant I could start the Most Wanted races whenever I wanted, despite only have played the game on PC for fifteen minutes.