In my opinion there are two main styles that most users adopt in Highlander play; passive and aggressive. Both are very viable, but what exactly does each really mean? The terms are thrown out a lot to describe many different players, but there hasn't really been any true definition. This is my attempt to finally give some definition to the terms. I've chosen these labels based on viewing other pyros, playing against them, and comparing starts of many pyros. Let's start with:
The Passive Pyro
In broad terms, the Passive Pyro devotes the majority of his attention to protection of both the combo and the flank, while staying out of most larger engagements until a significant advantage is achieved. From my own experience in Platinum, the vast majority of pyros fall into this category. Looking at logs, the majority of kills (and therefore damage) from a passive pyro will likely be against mainly flank classes. That is to say, you'll mostly be fighting scouts, soldiers, engineers, spies, and the occasional sniper. Passive pyros punish attempts from flank classes to get in, take position, and kill their more important teammates. During an uber push, they're more likely to stay back to help their team retreat if necessary, or try to kill enemies away from the uber. As a passive pyro you may take a more aggressive role when your team has significant advantage and is at lesser risk of being attacked by any flank classes. Overall, this playstyle can be somewhat compared to a passive scout in 6v6 who tends to stick directly with teammates, clean up over-extended and damaged enemies, and turn on the aggression once a large player-advantage is gained.
Before the July 10, 2013 rebalancing update, many passive pyros utilized the Gas Jockey Set to better fight 1v1s against scouts and soldiers on the flank. You can read more about this in the Gas Jockey section above. It is yet to be seen whether the changes to the powerjack will have a lasting effect on this style, but I would theorize that the inability to move quicker and dodge better while actively fighting will be a heavy downside.
The Aggressive Pyro
Contrary to popular belief, the Aggressive Pyro is more of a "pocket" style than the passive. In my definition, the Aggressive Pyro devotes the majority of his efforts to putting pressure and damage on high-priority classes. In other words, you'll mostly be shooting the demo, heavy, and medic (possibly pyro too--if you're running shotgun). There are decidedly fewer examples of this type of play, as I believe it is a higher-risk, higher-reward style best suited to highly aggressive teams. While you will obviously still fight flank classes if they extend into you, generally they're are not your primary focus. For that reason, your team's flank may overall be a bit weaker, as a pyro wall is an excellent way to stop encroaching flankers before they even start. The main goal of an aggressive pyro is not to roam and get picks, but to help his (or her!) combo win fights. You still play a semi-protective role, but in the aggressive pyros case, a good offense is often the best defense. Instead of coming in late to pushes, you try to lead or enter at about the same time as your combo. Your goal is to put damage on the players that will help you decisively win pushes, usually demoman, heavy, and medic. You might also use your airblast to simply move these classes into less favorable positioning as you go. Essentially you shoot the same things your own demoman and heavy do. You both listen for and make damage comms to ensure enemies are focused down. Like the aggressive scout, the focus is on more on kills that will swing advantages for your team.
Aggressive pyros will occasionally require more heals than passive pyros, which can at times be seen as a downside. It is important to understand your importance relative to your combo in this role. If you are hurt and your demo or heavy also need health, you are better served retreating to a health pack to ensure priority heals are given. You want to try not to take damage before a push or you might delay a significant advantage by requiring healing. Another downside is simply that you ARE fighting classes with both higher damage capability and higher health, possibly creating more difficult targets. As mentioned before, it is a high-risk, high reward style. You generally have to commit fully to fights, so you might die pitifully to tank classes, or you may ensure a kill that wins a push.
In my experience, the Gas Jockey set in the role of my Aggressive Pyro is not generally as useful as the axtinguisher. While in theory the speed bonus could help you chase down fleeing enemies during a push, your main targets are the heavy and demoman who have slower than average movement speed already. This usage is effectively null and void since the July 10, 2013 update, as the speed bonus is now only achieved while holding the powerjack, negating almost all offensive capability. In my experience this hasn't directly been an issue as you can generally use your airblast to trap heavies and demos, and will likely have to go through other classes before you can catch a medic yourself. In that stead, the axtinguisher is a very handy tool should the opportunity arise to insta-kill a medic, or take a huge chunk of health from a demo or heavy for either a kill or quick cleanup from your teammates.
The theory behind my definitions of these two styles were largely gained by comparing viewed gameplay with results in logs. The pyros I identified more as passive killed mainly scouts, soldiers, and spies in large numbers with the occasional combo class. Those I identified as aggresive had a more consistent spread of kills throughout, with a definite difference in combo-class kills in comparison to the passive.
Different maps are suited to different styles. The best example is probably payload and other attack defend maps. On these maps you might be able to use the aggressive style on offense, while defense almost requires the passive.
Whether you can run one style or the other might depend highly on your team as well. If your team plays a more patient game and waits for larger advantages to push, then passive is probably what you're going to be doing. Currently in Highlander most teams fall into a more passive category. The game is quickly evolving to favor the more aggressive play though, so we'll likely see more aggressive pyros in the future. If a team plays faster and pushes off of smaller advantages, aggressive pyro might work better.
It's important not to overstep your boundaries, so do not try anything that does not fit your own team. Both playstyles are very effective when employed correctly!