How much does it differ from D20 System Mechanics?
Very heavily. While Savage Worlds does have feat-like abilities called 'Edges' the method in which you earn them is different from d20 system. About the only thing really in common is that rolling high is always a good thing. Other then that, Savage Worlds is a Skill-based game. So that Fighter your playing isn't "Fighter 3rd level" but instead they have skill points in subjects lighting Fighting, Shooting, Climbing, and etc. The skills are very broad so that the Fighting skill covers all melee while Shooting covers any ranged weapon that isn't thrown. There are house rules for adding specific branches of a skill, but the developers really emphasize being "Fast, Fun, & Furious" over realism.
The differences are very large to list. Even just listing that there are no classes, but skills, other differences include: different attribute names and certain attributes folded together, main characters and NPC's have only 3 wounds, regardless of level. Minions have only 1 wound point. Almost every dice rolled in the game has a chance to 'Explode' meaning if you roll the highest number on a die (like a '6' on a d6) you can re-roll and add the next rolled result for a total, if that second roll comes up with the highest number again you roll a third time, and so on until you do not show your highest dice.
Why would I choose to run Savage Worlds over d20? Hard to explain. For my neck of the woods my rpg group I meet in person really only likes Savage Worlds after years of Pathfinder. I would say coming up with NPC's is easy and the book emphasizes that, unlike characters, a GM just make up what they feel the NPC needs rather than use build points to stat them out. The game is also very much a toolbox/hobby horse game that encourages a GM to make house rules (or buy other books that might add more meat to the skeleton to the game). For instance, in the core book alone there are no rules for magic items. Now, there is nothing to stop you from, say, using magic items from something like D&D (with a little bit of tinkering) but you could also by the Fantasy Companion which adds magic items to the game - so if you're a tinkerer type who loves houseruling or making stuff up, it might be a good fit.
Pros & Cons
Pro: Has rules for actions that players might have asked for or bugged about in d20 that aren't covered as well. Like 'Called Shots'. In D20 I've yet to see a set of Called Shot rules that really worked too well (like when a player says they want to hit the beholder in the eye specifically). Savage Worlds has rules for called shots and the effects they can have on the body.
Con (Maybe): The 'math' behind the game is apparently wonky given the explosion system. As one reviewer put it: The game is like chiseling with a jackhammer. Sometimes its slow, plodding, carving out a piece or two. Sometimes it supercharges and tears through stuff. An example is that our party faced a high end dark knight who had been corrupted by the Demons. The GM had put some time and effort to stat this guy's stuff. It was the big fight. At start of initiative one of our fighters won, got in close, called shot and then nearly decapitated the dark knight with a single blow thanks to explosions. The knight managed to 'Soak' (remove wounds thanks to a Bennies system built in the game) but he was on the ropes throughout the whole episode.
Pro (Maybe): Though Fast, Fun, Furious the game has a lot of nods to material like firearms. The core game includes rules for range and range penalties, Edges for shooting at long distances, scopes - basically if you ever ran a spy/military game and you wanted that one player to play a sniper, picking off targets at long distances at night with a silenced rifle to the terror of the NPC's around the victim - it can be more or less modeled in game, right down to the head shot that blows out the victim's brains. Obviously for a fantasy game that doesn't come up as much, but there are rules for blackpowder firearms like muskets and flintlock pistols. So! If you like guns in your fantasy and want to emphasize that they are deadly weapons, there are rules for that.
Con (Maybe): Magic is functional, but a little bit bland. They do have rules for flavoring spells with what are called 'Trappings'. An example is that there is a standard Bolt power. This is your usual attack ability which can fire several small bolts or one large bolt at the cost of Power Points. With the trappings system, and there some examples, you could add stuff like Acidic Corrision, Fire that penetrates armor or possibly sets the enemy on fire. You could make the bolt bees that fire out of your hand and deal poison damage to the target.
Let's have that simmer as-is and next post I'll talk about settings.