Leveraging your stamina to good effect is probably the vaguest area in Mafia Wars. There is a lot of benefit to beating up your rivals though and you would be remise to ignore this aspect completely. With the changes that went in to make a stamina point only cost a single skill point now, you can get more XP per skill point from fighting than you can from jobs though it takes a lot longer and the healing costs will make it a cash negative operation. Each conflict like this will generate from 1-6 XP randomly and relatively evenly spread.
It is worth noting that when it comes to fights, nothing ends up being more important than your mafia size. There are some players who have either purchased very large amounts of reward points, or even more frequently, leveraged an exploit to get an excessive number of reward points and have used these to get silly ridiculously large stats and sit in the 450-500 range of mafia sizes to trick people. For the most part though, it is very difficult to be successful at high levels without having the max 501 mafia size. For most players, this means searching Facebook for various mafia wars groups with "501" in the title and getting on massive join lists to boost their number of friends artificially. You can safely drop someone as a friend after they are in your mob and they do not automatically go away within the game. It can't be stressed enough the importance of growing your mafia size as quickly as possible and making sure that you have at least 501 weapons, 501 armors, and 501 vehicles.
The largest advantage to getting into large numbers of fights is that in any fight you win, you have a random chance to loot a random item that you have access to. How this table of items is generated isn't really known, but it does seem that the higher your level gets, the better items you tend to find from beating up other players. This can be an absolutely critical supplement to getting things like the Cell Phones, Blackmail Photos, and Illegal Transaction Records. Plus there is the added benefit that the more you fight, the better you get at it since you will tend to loot high level items as well.
There is some controversy over exactly how the attack and defense numbers are compared. One theory states that your total attack is compared to your opponent's total defense with some minor random amount calculated. The other theory is that your total strength is calculated (both attack and defense are added together for your items which have the highest attack values if you are the attacker). This second theory means that a weapon which is 20 attack and 20 defense ends up being strictly better than an item that is 22 attack and 1 defense. While there isn't any conclusive evidence one way or the other, personal experimentation makes the first theory look more likely.
This means that as you are going through your jobs, it can be worthwhile to stop and try to collect around 450 of the key items that make your attack and defense as high as possible. The downside to this approach is that you aren't making any progress on the job tiers in the meantime. Realistically, since fighting also has a chance to drop these items, it is only worth trying to stockpile once you have mastered all job tiers you currently have access to.
Currently the best equipment to outfit yourself in that comes from jobs are the Canonazo, Gaff Hook, Guerilla Squad, Armored Briefcase, Armored State Car, and Track Loader. Of course, Zynga rebalances these items quite regularly so you want to take a look at your Loot tab often to see where you can get the highest bonuses from. Once again, if you have friends which have been doing a lot of fighting, ask around about extras. With the extra loot drops from fighting it is quite common for someone who had 501 of an item to all of a sudden realize they slowly ended up at 600.
Robbing has gone through many changes over the course of the game. Due to various amounts of griefing that were accomplished through the system, it seems that robbing has been removed for the moment. Once a revamped system is put back in place, it can be analyzed for what is now possible.
Under the old system, it worked just like fights with the exception that both the attacker and defender's mafia sizes were capped by their respective levels. While this worked well for low level folk to keep the playing field level, it meant it was impossible to defend against an assault from someone who was over level 500 if your were under 400. Hopefully we will see something new and creative soon as this was a wonderful way to make money at low levels and start building up towards the large money achievements.