Character differences: appearance, personality, voice, and ammo carrying capacity, natural stamina, natural vitality, and skills.
You can take a look at each skill at http://deadislandwiki.com/wiki/Skill_Tree (one page) or http://deadisland.wikia.com/wiki/Skill_Trees (character pages), so I'll try to cover what MAY not and what WILL not be immediately realized from reading those. Here are descriptions of each character, in no particular order:
Fury: weapon: revolver, effect: auto-aim on fire (targets need to be on screen), team boosts, indefinite ammo, screen-clearer like Logan's.
Team-oriented with a beginning, middle, and end Survival skills that boost attributes of team-mates within range as well as bonuses from her Fury. Head-stomps count as kicks, so she can earn extra Fury on head-stomps, and head-stomps are bread and butter for every character from the time that it is unlocked (i.e. ASAP) until the end-game. The cherry on top is that fully upgraded Inspiring Kick is comparable to fully upgraded Grim Inspiration + Righteous Fire.
She can carry two times as much ammo as the other characters' default and her skills focus on getting more ammo. The skill ability to get an extra percentage of ammo whenever ammo is gotten applies to ammo crafting too. Be prepared to shell out a lot of money to stock up on hundreds (if not thousands) of bleach and metal scrap to craft your own bullets. She doesn't hit her stride until the middle of the game, unless you're making good use of Inspiring Kick + head-stomps. Guns don't feature prominently until between chapter 5 and 6.
Pro-tip: Coloured rarity firearms deal damage independent from their listed stat. The only way to find out a coloured rarity firearm's true damage is to test it. The "Make yourself at home" side-quest for Harlan Johnson is great for this because the docile Thug respawns if you don't turn the quest in.
Read more about Purna from Lastat27.
Fury: weapon: throwing knives, effect: auto-targets, click to throw, indefinite ammo, high RoF, screen-clearer like Purna's, the only Fury that doesn't let you run in it.
Jack-of-all-trades, with random skills like two skills that boost from being drunk, and three milestone Combat specialization skills (top, middle, bottom) that boost different weapon types. Economical throw (splash damage on throw) is one of his most important skills. His end-game involves the special mindblowing and plaguebearing military knives, and other such weapons which highly benefit from Economical throw. Such items are expensive to repair, but throwing a weapon does not drain its condition. Like Purna, Logan doesn't shine until the mid-game, when he can get his hands on the aforementioned knives. Team orientation: Nothing explicit.
Fury: weapon: fury knife: short range, fast RoF, effect: increased severing.
Highest natural stamina, lowest natural vitality. Glass cannon, fragile. People say that she has the highest damage output. She can build Fury quickly. At the end-game, she can build Fury from 0 in three strikes/kills. Knock-out attack can be performed with fists.
Her most team-oriented skill is the ability to heal more (not just from med-kits), but this comes little into play. It's negligible because, unless you're duplicating med-kits or have adopted a strictly altruistic attitude with med-kits, you'll have few to spare. A dying player can't revive themself, so I am med-kit altruistic. Secondly, the best time to heal others, relative to the patient, is when they're on the ground at 0 health (i.e., dying), but that usually occurs when they get mobbed, and rushing in to heal them before their few seconds are up is a dangerous endeavour to fragile Xian Mei.
Fury: weapon: fury fists: technically brass knuckles, slower than normal fists, effect: max mêlée range, more force.
Highest natural vitality. Tanky. Has two skill-based methods of getting zombie heads to the ground: knock-out attack and tackle. His most team-oriented ability is Decoy, which causes zombies to prefer engaging him over other players, i.e. draws aggro.
Recommendation: Sam B. for beginners, because of his hardiness, his specialization in the weapon type that requires the least maintenance, the convenience of his tackle, and the fun of Impact (blunt shock) weaponry.
Side-note: This information is for the discerning individual. In-group favouritism, satisficing, and status quo bias prevents players from picking the best character for them. I present this information so that players may become informed of the different characters in-depth before making a commitment.
How am I not biased? I've played each character to the level cap and try to play all equally.
There are few people who play their character properly at the end-game. E.g., Sam B. swinging a sharp-type weapon, not being Purna but wielding a shotgun as your main weapon, not being Sam B. but swinging a homerun baseball bat, or playing Logan but only throwing just to confirm to yourself how ineffective throwing is.
Any character can dabble in what other characters are supposed to specialize in, but I assume that people aren't doing what their character specializes in because they can't stomach the idea of raising another character to a sufficient level to experience the other character's end-game, and complacency makes them stick to their main character which probably happens to be their main character solely because they happened to choose that character first.