Player factions can quickly rise to be more prominent/influential than DM factions - at least in the player side of things. DM factions will, obviously, always (?) be able to count with certain very powerful NPCs, but don't underestimate what a good player faction can do. Here are a few points that might add to the discussion:
Dependable Players: This is the most important point of all. When making a player faction, make sure you pick people who are going to be logging on, and doing things. This is not a carte-blanche statement for people to ignore the newbies - sometimes they're the ones with the most enthusiasm, and can help get things going very quickly. Pick your players well, and your faction will thrive.
Characters with similar IC goals: This one is much easier if you make a player faction that has a broader appeal to the character-base - a mercenary company who will offer to hire just about anybody will enjoy far quicker success than, say, a wizards' covenant. Try and broaden your appeal as best as you can - if you find your faction is too restrictive in its membership, try and hire people to do smaller, less important jobs, or try to open a different job for different characters. A wizards' covenant that only accepts wizards might be awesome, sure, but I promise you it will have a much harder time surviving its first few weeks than a group that decides it's a good idea to hire grunts as, say, bodyguards. To keep it simple: Find roles in your organization that can be filled by just about anyone - people will tend to stick around if they see they're actively contributing to the success of the group, even if they're not top dog.
Numbers are the most impressive way to recruit: Pretty self-explanatory - nothing says, "we're an up-and-coming, interesting and fun" player-led faction like a group of six people walking around in uniform. It sounds shallow, but, really, a lot of the 'presence' of the DM factions comes down to the fact that there's lots of people wearing the same clothes, going places together, and doing generally the same things. People are drawn to groups that look like they're tight and know what they're doing.
ALWAYS recruit: If you're the leader of a top official in a player-led faction, welcome to my personal brand of hell. It's a nightmare (albeit a very fun nightmare) to keep everyone on board with you all the time. People are going to disagree for all sorts of reasons, characters are going to die and people are just going to quit the server or the group for one reason or another - which is basically a fancy way of saying, the 'mortality rate' of your members will ALWAYS be bigger than the 'natality rate' if you don't actively recruit pretty much all of the time. Every scripted quest, every DM event, every talk in the tavern is a chance to get to know someone else's character, interact with them and get them to join you.
Keep things simple: No point in dreaming up a sixteen-tier bureaucratic juggernaut of a faction if you're only going to have six, seven members -- let's face it, it'll be ridiculous, cumbersome and boring.
Delegate: If a faction cannot function without its leader online, it's either a small faction that hasn't been fully structured yet, or something is badly wrong. The last thing you want is for the people in your group to 'go about their business' when you're not online. If they pledge to be in the faction and to help the faction, they should keep working towards the goals even when the leader is not online. The best way to ensure that this happens is to give everyone a job, and quickly identify the strongest lieutenants in your group, so that you can give them the authority to make the calls when you're not there.
Work up an M.O.: This is the hardest, but the most important. The reason why some PC factions work like well-greased machines, and others die within days of their inception is simple - the ones that work have things to do. What do I mean, 'things to do'? It's simple - whenever someone comes up with an idea to do something, that faction can quickly spring up a plan to do it within the framework of the faction - anyone can act on a DM tip to go look for some hidden treasure in the middle of nothing with a group. Only a well-oiled, excellently-structured faction can go look for hidden treasure with a well-balanced, motivated, trustworthy and strong group, within FIVE MINUTES of the DM pitch. It's simple - make sure your group is -always- ready - be it combat-ready, or whatever-it-is-they-do-ready. If you decide to put together a troupe of artists that are against the establishment and will constantly perform happenings throughout Sanctuary to undermine the power of the Status Quo by bringing awareness to the people of just how fucked up their lives are, then make sure you can be ready to go with whoever is in your faction, within five minutes of something. Nothing says 'We own' like a group that can get together and work proactively towards the same goal within five minutes.
Obviously, all of these depend on the luck of finding like-minded characters to join your own in game. But when things look bleak and no one seems interested in your idea, then it's time to go back to the drawing board and think it back up.
I hope this helps.