I have met two types of options market makers: the ones that like to sleep at night but bleed slowly (long gamma), and the ones that have never seen an option they like (short gamma).
The later don't really sleep well at night - you could understand how these guys make money, but like enjoying a hot dog, maybe you are better off not knowing how it is made. The ones that are successful imo know when and what to be short gamma, and what not to be. But other than 2008, short gamma rules the options markets.
The way you trade is hugely influenced by your cost structure and the kind of flow you are likely to see. Remember, options are mostly used by large institutions as insurance (although I think hedge funds are now (always ?) using them to enhance returns by using money (and therefore leverage) more efficiently). This means that generally, market makers tend to get the part of the distribution that the "market" doesn't want. So if you get Bank Of America paper, you are likely to trade one way. If you are mass quoting options and that is where most of your fills come from, you are likely to trade another way.
You guys always want to know what the holy grail is. The holy grail is someone giving you so much edge that you can work to turn that edge into a box by working the synthetic equivalent side of the flow you are getting (other than some insight into arbitrage opportunities, but usually that is limited in the size you can do). Outside of that, it is style and cost structure. Most people like to run their trading like a business, and that means mostly leaving with more money than you came into the day with. That means usually selling more options than buying them. That works, until 2008s come along and pulverize everyone in sight.