This right here is a lengthy topic to cover, most of the factions are shades of gray( or grey if you're not from USA) And have at least one redeeming thing to them,
The Hegemony might be a militaristic, way overly aggressive administration but it also does a lot of good, it provides incredible amounts of stability, and regularly obliterates pirates who would otherwise harm,maim, or kill civilians and other factions. And to us that may not seem like much, but until the 14th battlegroup showed up the sector was basically more lawless than the wild west in the USA.
The Church of the Ludd can be a bit harsh at times ( see CULT of the Ludd) but generally they just make food, and other basic commodities. Think of them as space Amish. And it's not like they want you to die constantly, ( again see CULT of the Ludd for that)
The Tachyons are a giant space wal-mart, they care little for humanity, they just want their money and for their company to remain solvent. The military is run more like our modern day military with a chain of command with the top being the Director of War. The military side is probably kept separate from the side that researches tech and what not. However the Tri Tach does still keep the peace around it's systems so there is the stability and safety that provides for the common man.
The independants are just that, although presented as one faction in game, each world is technically independent of each other as well.
The pirates are well, pirates and not the fun, Jack sparrow kind ( well some of them might be) But the actual pirate kind; killing, pillaging, and kidnapping as they please. ( and then being blown up by us or the hegemony)
I actually know very little about the sindrian diktat, a lot of people seem to compare them to nazis IF this is truly the case then count me out of space nazi town.
So what group do i throw in my lot with? Well usually i go with the tri tach ( i too love me some high tech ships with lasers) But i can see the good the hegemony does and if i was actually in the sector I'd probably sign up the hegemony military, or at least live on a core world/station.