I've had three different characters so far, and sided with all four factions. I roleplay, so most of the differences between how I play are down to the personality of my characters. They have their own little "quirks" and ways of dealing with quests. I keep in character, even if following certain "rules" I have for them means missing out on stuff. Like not being able to pick up a good legendary weapon, or never getting all the companion perks on one character.
Sorry, this is going to get pretty long. ^^; I'll keep the spoilers vague.
Robin - Male SS. Railroad ("canon" ending. Initially sided with the Institute).
First character. Good natured guy. Avoided violence whenever possible. Helped others a lot. Typical approach to these games for me. As I followed the main quest, I planned to side with the Railroad. Ended up getting caught up in the "finding Shaun" side of the story, and sided with the Institute. I recently started a new save to get the trophies for siding with the Railroad, and decided to bring Robin back to make up for what happened the first time.
I didn't flesh his character out much on the first playthrough because I was still getting used to things and experiencing the story for the first time. Second time, I thought more about what I wanted to do with him. He didn't romance anyone on the first playthrough. Second time around, I got him together with Curie. I saw Robin as a protective type, and felt he'd feel obligated to stay close to Curie after her personal quest. He probably didn't except to get THAT close...
I really enjoyed using the Power Fist as one of his main weapons on the first playthrough, so I decided to focus on melee. Used pistols whenever I needed something with a bit more range. Decided he wouldn't use chems or alcohol (with an exception for drinking a bottle given by Desdemona at the end of one RR quest). Rarely used power armour. Typically wore the surveyor's outfit (or Reginald's suit) with ballistic weave and Grandpa Savoldi's hat.
Gavin - Male SS. Brotherhood.
Third character (leaving my second for last). I knew what I wanted to do with him from the start. Rude. Mean. He wouldn't help anyone unless he thought there might be something in it for him. His personality softened a little in time, but overall he continued to only looked out for himself. Or fellow Brotherhood members. Largely ignored the Minutemen after saving Preston and company in Concord, and did the bare minimum of work at Sanctuary (during which he was pretty rude to Sturges). Only worked with the Railroad and Institute as long as it was to his advantage, and the Brotherhood's. He was a devoted Brotherhood of Steel member and followed Elder Maxson's orders without question. Well, except for that one time he didn't...
Changed his hair (style only) after meeting Maxson for the first time. Gave him some scars after tough battles.
He used chems, but only when absolutely necessary. Usually just to give himself an edge in a really tough fight.
Gavin almost exclusively used the unique laser rifle given to him by Danse, after adding some modifications of his own. Being so loyal to the Brotherhood, he favoured their uniform and combat armour. He also used power armour a lot. Personally, I'm not a fan of the PA and don't use it unless I have to. But I try to stay true to my RP plans, and it fit Gavin's character to use it a lot. I might not think much of PA, but he loves it. And it was actually fun from an RP perspective. I'd do it again.
He romanced Danse. Guess he really admired the guy's devotion to the Brotherhood. In spite of certain events.
Natalia - Female SS. Minutemen.
Ohmigosh Natalia. What a mess she was! My second character, and the first to romance anyone. I left her for last because things didn't go the way I planned with her. The plan was to play her as being entirely focused on finding her son, and not being able to accept what became of him when she finally found out. She'd be mean, sarcastic, and self-centred. Her only reason for helping any of the factions was because she realised each of them had the potential to help her. I was going to have her side with the Brotherhood, and romance Danse. Maybe even multiple companions.
It fell apart early on because Natalia is frequently sarcastic, and the delivery of the female SS's sarcastic dialogue changed how I viewed her. She was coming across as a more playful type, and I couldn't imagine her becoming seriously involved with the Brotherhood, or Danse. So I decided the Railroad might suit her more, and maybe MacCready as a romantic companion. He likes sarcasm, after all. Wait! No, I'll have her hang around with Hancock instead. I neglected him a lot on my first playthrough, and it'll probably be funny romancing him. But it turned out I loved his backstory, and his reaction to being romanced was adorable. Natalia made Hancock my favourite companion, and he made her my favourite character to play.
I had problems with a Railroad quest late in the game. Hancock kept getting killed. I couldn't seem to keep him safe, and didn't have a save old enough to send him away while Natalia dealt with it alone. By this point, I couldn't imagine letting Natalia carry on without Hancock, but the glitch did me a favour. It convinced me to restart Natalia and play her RIGHT. I also decided to have her side with the Minutemen so she could keep Hancock by her side without risking his life. Turned out they suited her better.
Natalia is a good-natured and friendly person with an odd sense of humour. She is rarely rude to people, but often makes sarcastic remarks and isn't afraid to make her feelings known (specifically, she's very blunt towards Maxson when they first meet). While she does try to resolve things peacefully, she has no problem taking the violent approach with those she feels deserves it. She can't walk away from a person in need and often puts herself in harms way while helping others.
A lot of her quirks revolve around ghouls. She first heard about them from Preston when she met him in Concord, and what he said made a strong impression on her. The first friendly ghoul she met was Hancock in Goodneighbor, and she's intrigued by him from the start. With one or two exceptions, she's kind towards ghouls. She will kill ferals if necessary, but prefers to avoid doing so. She won't loot from ferals, with an exception for legendary "Ghoul Slayer" weapons. She doesn't want them getting into the wrong hands. Any useful ones get modded and given to people she can trust to use them responsibly. The rest get sold to KL-E-O or Daisy, who she feels can be trusted with them. I also get the "Ghoulish" perk for her as soon as possible, although I imagine it disturbs her when ferals become allies because she hates seeing them fight each other.
After Hancock's affinity is raised enough that he starts using the "we should find a way to turn you ghoul" line, Natalia gets lax about radiation exposure. No healing rads until they're taking up about a third of her health. No protection against rads unless levels are SERIOUSLY high. I don't think anyone has the heart to tell her she's more likely to kill herself...
Natalia will use any helpful chems to give her an edge in a fight. She'll also use Graqe Mentats to her advantage in trading, except when dealing with traders she likes and respects. She rarely drinks alcohol, but keeps some around for recipes.
Her preferred weapon is a modded combat shotgun (I'd love to find her a Ghoul Slayer one, which she'd use when she has to kill ferals), with a 10mm pistol and melee weapons (usually Deathclaw Gauntlet or Power Fist) as backup. She wears the 111 vault suit with modded leather armour. The only time she used power armour was at Concord.
And that's it so far. I'm planning on making another female SS to take over Robin's place with the Institute. Got a few ideas for her. But before I do that Natalia needs to go build some robots...