This post is not so much about the differences between the factions ---- we all know that topic has been debated to death in many threads! Rather, it's a post asking whether you play with solely in-character knowledge or if you "meta-game", using knowledge that you, the player, have.
I was agonizing about whether to side with the Institute or Brotherhood recently, but at level 102 I figured I'd better go ahead and pick one. As I was treating myself to a "final" tour through the Institute, I found myself thinking, "Hey, these people aren't so bad". Everyone was polite (except that one Doctor who objected to me becoming Director, but I let him live so he was grudgingly okay with me). Everyone congratulated me on bringing in the rogue synth raider from Libertalia (forget whether I sent him home for reprogramming or killed him: in either case, the treat was removed).
In-character, I couldn't really find any reason to object to the Institute people. By contrast, my dealings with the Brotherhood had always felt like they were trying to boss me around, treating me like a useful savage. Perception, I know, since if you join the Brotherhood you get promoted to just under the top dog.
When I was debating which faction to side with, I was thinking in terms of meta-gaming benefits and knowledge. Like, I reasoned that having the Brotherhood as my ally would mean I could use (and not be fired upon by) Vertibirds. The Institute Synths don't really pose near as big or ubiquitous threat as the Brotherhood. But that was a meta-gaming consideration. My ~character~ would not really care about having access to Vertibirds or try to pick the least-annoying threat.
Likewise, from my character's point of view, her son was perhaps little detached and anolytical, but in conversations with him, he always seemed reasonable (so far). When he asked if I would mind destroying the Railroad, he listened to my questions and objections. And when he wanted me to destroy the Brotherhood, he agreed with me that whatever we did, it should minimize the casualties among the Commonwealth. Sounds reasonable, and having met the Brotherhood, I had to admit, the two factions WOULD eventually butt heads. So something ~would~ need to be done. And while the Brotherhood ran patrols and so on in the Commonwealth, fighting supermutants and ghouls, my personal interactions with them had suggested that they were very me-me-me exclusionary, wanting to hoard tech for themselves.
Granted, the Institute wasn't exactly eager to offer their technology to the Commonwealth --- they wanted to stay separate and protected, and I can understand that, given the history of the time they DID try to integrate with the surface world. But for example, the Institute recruited a Commonwealth genius to join them, which he appears to really enjoy, so they are not so exclusionary as the Brotherhood would seem to be (to me).
By contrast, my male character has (thus far) not had any dealings with any factions other than the MInutemen and in a nod to meta-gaming, I am going to sort of steer his personality so that when he meets the Brotherhood he will see them as fellow ex-military and performing a noble service because these savages clearly don't need to have access to world-destroying tech (again!).... and when he meets the Institute, I won't be playing his discovery of Shaun's real age as soft as I did with my main: he will be PISSED. If he were to take the time, he might come to see their side of things, but he's ex-,military, "just" saw his wife killed and son stolen and has suffered through the Wasteland and he will be disgusted by the selfish opulence on display in the Institute.
It's a fine line between letting your meta-gaming knowledge influence your in-game character personality in ways that do not fit the character concept you ~had~ and using meta-gaming knowledge to ~steer~ your character concept. In a way, I sort of boxed myself into a corner by developing my first character's concept/personality as I played the game (having not finished it at that point). The character already existed by the point I started to weigh meta-gaming considerations. This second (male) character's personality and concept will be ~determined~ in advance by my meta-gaming knowledge. But since he'll be going into the game world with that pre-determined end-goal, it will SEEM as if his actions in-game are perfectly in-character and logically self-consistent.
Long-winded way to say, I figured out which faction I finally want to align with in this, and my next, playthrough.