...really isn't that different than it used to be. I'm Raking and Ripping less (because they last a lot longer now), and Ferocious Biting more. But other than the opening 10 seconds or so of the fight, the priority order hasn't really changed from what it used to be.
One minor difference is that with the change to bleed/DoT clipping, you no longer have to wait for Rip or Rake to expire to refresh them. You're no longer at risk of losing that last tick. Now if you refresh a bleed or a DoT between the last tick and the next-to-last tick, the duration gets extended when refreshed to include the last tick. I know that's confusing, so let me paint it this way:
Rake (unmodified) lasts for 9 seconds and ticks every 3. So you apply Rake, wait 3 seconds, tick. 3 more seconds (6 total), tick. 3 more seconds (9 total), tick and the bleed expires. It used to be that if you refreshed Rake before it expired, it would reset back to the full 9 seconds and you'd have to wait 3 more for the next tick. So if there was 1 second left and you refreshed it, now you've gone 5 seconds between ticks (2 since the last and 3 until the next).
The way it works now, if there's 1 second left and you refresh it, it adds 9 seconds. So it will now last 10, and when the timer goes down to 9 you get the tick that you would have gotten on expiration.
(This may true regardless of when you refresh it, not just between the last two ticks. Either way, when refreshed, you're adding the duration to the time until the next tick, not the total remaining time.)
Clear as mud? If the details are still confusing, just take my word for it: the idea with Rake and Rip is now to refresh them between the last 2 ticks, rather than after they've expired.
After that one change there may be a couple more, depending on your spec choices.
If you've specced into Stampede, you may be opening quickly with a Ravage where you normally wouldn't.
If you haven't specced into Feral Aggression then you may be hitting F3 more than once and making sure you refresh it before it expires to avoid having to hit it more than once again. (This usually isn't an issue, as there's always some downtime in the rotation while waiting for Energy to regen. I always fill it with a quick F3.)
The other change that comes into play is if you've specced into Nom nom n...I mean, Blood in the Water. Once you get to the last 25% of the fight, your FBs will automatically refresh your Rips meaning the only time you should Rip is if it's dropped off completely. Which hopefully won't happen.
And that's about it. Right now kitties are putting up disproportionately big numbers, so go out there and enjoy them while you can before you get smacked with the nerf bat.