Someone did a study of 1500 games
Runner won 55% of the time, Corp 45%
They also broke it down by each runner vs each corp
Criminal won 62% of his games
Anarch won 52%
Shaper won 48%
HB won 50% of its games
Jinteki won 41%
NBN won 39%
Weyland won 51%
The early game favors the Runner. The Corp has no defenses and is in a rush to protect multiple targets. In addition, he also has to set up additional servers that the Runner can hit. It is only by creating more stuff for the Runner to raid that the Corp can win. And though the Corp starts the game defenseless (which is why he gets the first turn), the Runner starts the game ready to attack (you don't need icebreakers to steal agendas).
The late game favors the Corp. Surviving the early onslaught, he'll probably have his economy up and running afterwards. Rezzing ICE is a one-time expense and it stays up and running, while the Runner has to pay his icebreakers each time he uses them. By then, the Corp will have built up multiple layers of ICE on each server, while the Runner has to struggle with marshalling enough resources to penetrate the Corp's defenses.
The reason for the statistics above is that Criminals, HB and Weyland have advantages when it comes to speed.
Criminals have fast cash (Bank Job, Easy Mark), can cripple the Corp (Account Siphon) early in the game, can expose or evade ICE (Forged Activation Orders, Inside Job, Lemuria Codecracker, Sneakdoor Beta). Those are cards that allow them to run frequently in the early game, even if they lack icebreakers.
On the other hand, both Anarchs and Shapers need time to build up. Anarchs need to organize their programs, whlie Shapers need to gather the resources to ultimately overpower the Corp's defenses. They still have the inherent early game advantage of the Runner side (and cards like Demolition Run, Medium and The Maker's Eye), but their stuff doesn't support it as much as the Criminals' do.
Weyland has huge economic advantages. Their ICE are pretty solid, especially where they can be advanced. When it comes to bagging the Runner after tagging, they can win the game decisively and suddenly thanks to Scorched Earth.
Haas-Bioroid's 1st identity (currently) gives the faction a good second place in economic advantage. Their bioroid ICE are cheaper to rez because of their penalty while being crippling in effect (brain damage, program destruction) or at least just straight up stopping the runner (almost all have the "End the run." subroutine). Their ability to do extra actions really helps (though I still think Shipment to Mirrormorph is sub-par), especially when it's time to rush the scoring of an Agenda. Lastly, they don't really do traces which is actually in their favor since it forces them to save their credits for other things.
NBN is supposed to be the agenda advancing specialist among the Corp factions, but I think that their ICE being mostly non-lethal and their lack of money generation hinders them. Jinteki really, really, really needs to coordinate its ICE for their defenses to be effective. While their net damage and trap-laying can be lethal, most of their ICE can't end runs. Ambush and Project Junebug are nasty, but not as decisive as Scorched Earth.
TLDR version: Criminals win most because they push their early game advantage. HB and Weyland succeed the most because they can go faster than other factions in setting up defenses and starting to work on their victory conditions early on.