Robbing is now in game for a small subset (probably about 10%) of the gaming population. Here is how it works:
When going to the robbing screen, you are presented with 6-9 possible properties to rob. Usually a few properties are listed as "easy" while a few always seem to be listed as "hard". Despite this, if you have a strong fighting account, you will almost always win your "hard" matches. If you have a really weak account, you can still lose "easy" matches. It doesn't seem to be a reliable gauge of your opponents weaknesses. If you're strong, you'll win. If you're not, you probably won't.
Also note that your board changes while you are away. As predicted, you will need a good bit of stamina to really take advantage of this new feature (200 stamina seems about right). Good thing the chop shop has a +5 stamina car, so even if you are firmly entrenched in a high level, fighting based account, you can still easily pick up tons of stamina.
If you successfully rob each property on your property "board", you will get a bonus XP reward. I've seen as high as 500 XP. This makes robbing a great way to get experience points, assuming your account is strong enough to rob other players.
Additionally, as you rob, you have a chance to get bonus loot pieces (random loot pieces, sometimes high end, just like with fighting) and also a chance to get robbing collection pieces. Here's what they do:
Tools of the Trade Collection
Pieces in set: Lock Picks, Diamond Drill, Flashlight, Walkie Talkie, Safecracker's Stethoscope, Black Ski Masks, Grappling Hooks
Reward for vaulting: +20% cash and items from robbing
Stolen Diamond Collection
Pieces in set: Hope Diamond, Koh-I-Noor Diamond, Great Star of Africa Diamond, The Orloff Diamond, The Sancy Diamond, The Idol's Eye Diamond, The Regent Diamond
Reward for vaulting: Improve odds of successfull robberies by 10%
The collections are pretty solid, especially if you rob a lot. Note that with the Stolen Diamond collection, even a weak energy account can successfully rob even the toughest opponent. Bringing back the RNG!
At any rate, it's nice to having robbing back. I'm not sure when it will be available for everyone, most of my accounts do not yet have it (even the ones with properties).