Battle System:
Starting with FFXI and running through the original XIV, the battles had been... boring, for lack of a better word. It was basically you could do a fight while watching TV, looking over every 45 seconds to see if you have enough TP built up to hit your macro.
FFXIV battles are much more like World of Warcraft (or other modern MMOs.) The red circles show up to show what the area of the enemies attack is (if it's a cone it will show the cone, etc.) and you have to avoid it. The pace is much quicker. You have your hotbars to show your skills, and the interface is resizable (Medium-Large-Small sizes for each window.) There are combos between some of your skills, so you get used to using them in a certain order - but there isn't a need for 15 hotbars on your screen like in WoW. I'd say it's a pretty happy balance between being boring and being overloaded with too much to do.
Classes:
Okay, so there are jobs and there are classes. You start out with basic classes, and once you hit 30 in one class and 15 in another (the combinations vary) you can undertake a quest to gain a job. The job is just a crystal that you equip, and it gives you access/turns you into that class while you have that gear set on. Each class is tied to a weapon-type.
Basic Classes
Disciples of War
Gladiator - Heavy plate-armor wearing, Sword n' Board tank.
Pugilist - Hand-to-Hand DPS.
Marauder - Heavy plate-armor wearing, 2H Axe DPS.
Lancer - Polearm-wielding DPS (may be able to offtank in a pinch if the tank dies)
Archer - Ranged DPS. Name speaks for itself.
Disciples of Magic
Conjurer - Your basic Healing class.
Thaumaturge - Your basic caster DPS class.
Arcanist - Pet-class [2 versions of Carbuncle] caster (mostly damage, does get a small heal and pet heal as well.)
Jobs
As I wrote earlier, jobs are attained after reaching 30/15 in your set classes. These are more of the classic FF classes - more specialized than using jobs.
Paladin - 30 Gladiator/15 Conjurer. Tanky with some heals. The defensive mainstay.
Monk - 30 Pugilist/15 Lancer. Hand-to-hand beatdown specialization is their game.
Warrior - 30 Marauder/15 Gladiator. A bit tanky, but mostly 2H Axe DPS. Some think they can tank, but it's not always preferred.
Dragoon - 30 Lancer/15 Marauder. Some sweet DPS with jumps and polearms. No pet this game.
Bard - 30 Archer/15 Pugilist. Ranged DPS with a few party-support skills mixed in.
White Mage - 30 Conjurer/15 Arcanist. The healer of healers.
Black Mage - 30 Thaumaturge/15 Archer. They make things go boom.
Summoner - 30 Arcanist/15 Thaumaturge. More pet&DoT-based DPS. Pet's are Ifrit-egi, Garuda-egi and Titan-egi.
Scholar - 30 Arcanist/15 Conjurer. Fairy-pet type based healing. Also provides some party buffs.
The Community
Well, the NA/EU community is pretty whiny, but that's to be expected since they can't log in. I haven't had any issues running into bad groups of people on the JP server I play on and I'm in an English-speaking Linkshell (basically chat channel that you have to be invited to, used to be their version of guilds) and Free Company (what FFXIV:ARR calls their guild system.)
PvP
Not my cup of tea in MMOs, I dislike PvP quite a bit. I don't think it's implemented yet, but the only thing there will be is arena-type PvP. Nothing open world, thank god.
Story
I've enjoyed the story so far, but I don't pay too much attention to it. We'll see how it goes when I reach end game. It's been very interesting so far, but I can't give a plus-or-minus to it since I don't play MMOs for the story.



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