When attacking, each member of your mafia picks up the most powerful weapon, vehicle and armor, in descending order, until they all have one of each, based on selecting the highest attack value items first.
The same is true for defending, except it is the defense value of the item that counts.
A mafia with 500 members and enough equipment to go around can attack with 500 weapons, 500 vehicles and 500 armor (remember, most armor has an attack value, too.) That's 1500 attack items mustered against an opponent.
If the opponent has a 200-member mafia and enough of each type of item for each member, they can still only muster 600 defense items. Unless the attacker is using very weak items and the defender is using very powerful ones, the defender doesn't stand much of a chance.
Of course, the aggregated equipment scores are modified by how you assign your skill points to your personal attack and defense, and you must account for any boosts used. So, a 200-person mafia with 700 skill points dedicated to defense (and some decent weapons) might hold up against an attacker with only 120 skill points assigned to attack.
Of course, 500 members are not very useful in fights if you do not have enough equipment to go around. You must have six types: attack and defense vehicles, attack and defense weapons, and attack and defense armor when calculating how well equipped you are. Note that some equipment serves well for attack and defense, while some is better in only one capacity.
Another benefit of a larger Mafia is seen when you view the Live Feed. If you are there hunting for job opportunities and bonuses, a bigger mafia will mean a bigger feed with more options. It also means more people will see your requests for help or wish list items.
IMPORTANT: Facebook (and maybe MySpace, I don't know) sets your maximum feed participant number to a default of 200. You want to raise that by going to the bottom of your MW page and clicking "Edit Options," then changing the number in the box. Raise it higher than you expect your mafia to grow.
It must be said that larger mafias are more difficult to manage and can bring the game to a frenzy of activity that is not for everyone.
Note that you can add more than 501 people to your mafia, but only you and your 500 highest-ranked members will be active. (This last point should be confirmed by another contributor before it is considered reliable. Perhaps the game picks only your first 500 members, or picks at random -- this must be clarified.)