Many people split pvp in EVE into two types. Some categorize by the size of your fleet, claiming that there is a 'small-gang' mentality and a 'large-fleet' mentality. Some split it by region, sometimes in the same breath -- the "null-sec pvpers" vs the "empire pvpers."
The truth of the matter is, there are two primary sets of motivations that drive pvpers in EVE, and these dictate where they fly, how they fly, how large their gang is, their strategies, and the size of their gangs.
These motivations, simply put, can be broken into "goal-driven pvpers" and "pvp-driven pvpers."
Goal-driven pvpers are all about some end result or objective that is outside the pvp itself. This could be taking a system, killing a pos, or any number of things. Their whole focus it to meet their objective. Their strategies are based on their end goals.
Much goal-driven pvp happens in null-sec, because of the current sovereighnty game mechanics. This is where people fight over space, stations, resrouces.
Also, goal-driven pvpers are not particularly concerned about 'equality' in a fight, since their primary objective is to win, not to have a good pvp moment. Of crouse, having good pvp in the meantime is always nice, though again, they usually will not hesitate to completely overpower their enemy in the interest of achieving their actual goal.
PVP-driven pvpers are all about the fight. They're in it for the pvp. They wish to kill things, and they're not particularly interested in anything except having a good fight. Frequently, they will have surface level 'objectives' for killing POSes, POCOs, or the like, though their primary objective is to get a fight, and their strategy and fleet make-up reflects this.
Much pvp-driven pvp happens in low-sec and npc null-sec. Because of the lack of sov mechanics in these places, it is easier for GF seekers to find the fights they want.
PVP-driven PVPers are very concerned about the quality of their fights. While they are always interested in getting kills no matter the circumstances, the most satisfaction comes when you win a fight that is somewhat equal on both sides. They tend not to overpower their enemies, as this would not encourage a fight. In many cases, they fight the same people frequently, and because of this, a silent code of honor exists so that fun fights can be had in the future as well.
The Tension Between the Poles
There is often a lot of name calling between each side of pvp. Goal-Driven pvpers frequently look at pvp-driven pvp as lacking. "The big guns fight over space" is often their attitude.
PVP-Driven pvpers are often disgusted with goal-driven pvpers. "They blob their enemies. There's no skill in that."
The truth of the matter is, comparing the two styles is like comparing apples and oranges. They are similar, but very different. Trying to enforce your own set of 'rules' onto a different set of motivations altogether is like putting a square peg in a round hole.
The Great Marriage
In addition to enforcing your own style onto the very different motivations of another pilot, you also have to understand that these two motivations are more like poles. While you label people 'pvp-driven' or 'goal-driven' the truth of the matter is we're each a little of both. We lean heavily toward one side or the other, but there's always a little of the other in us.
Corporations who can balance these two motivations often tend to enjoy a higher longevity. If they push themselves to be somewhere in the middle, seeking both good fights along with the achievement of goals, then failure or disappointment at any one thing will not crush them. If they lose their space, they will not give up and disband as easily. If their fights dry up, they have other goals to seek out.
The Great Divide
I believe that PVP in EVE is 'polarized' much more then it used to be in years past. I can see it in the issues that are raised and discussed on the forums. I can see it in the recruitment channels with people looking for 'corps that don't blob' or 'pvpers who can solo' or 'pvpers who are familiar with null-sec fleet tactics.' I see it in the platforms of the CSM candidates.
People are shifting, aligning themselves into makeshift 'sides' and a new layer of EVE politics has been born.
Some may see this struggle as a problem--as something to be overcome.
But every day, as I see this struggle heighten--as pilots argue and hate and cry and rage and love and spy and point fingers, and form sub communities, and accuse, and explain the 'right' way to do some thing, or fit some ship, or battle some enemy--
I think, what a wonderful sandbox this is.