Great question :)
Well for myself, I genuinely enjoy pretty much every aspect of the game. The crafting is extremely enjoyable, as is the gathering, and combat is for the most part a pretty fun, interactive experience, with the potential to be very dynamic by switching out classes and abilities.
The way I see it, this game, in its current state, is only going to have lasting play appeal for a certain niche of players.
People who want to focus on a single class, and/or crafting class, and who play for a long time each day are quite possibly going to get frusterated, because the leves and grinding will get very repetitive for them. If they don't have a good social base in the game, they will almost definitely get bored and leave, and quite possibly have their frusterations augmented because of the general portion of their life focused on the game, which, let's be honest, is far from complete in it's current form. The other type of person I believe will have issue with the game is the type of person who wants to level up every day or two. This is near impossible past level 15 or so unless you are literally on it all day, and even then it would be a tedious grind-fest.
So who does it appeal to?
FFXI players who don't have time to play for hours on end anymore.
People who don't get bored with grinding and who play for long periods of time each day.
People who enjoy social elements of a game.
People who only play for a few hours a day, and are content with a levelling rate of 2-5 days (beyond level 15)
People who are looking for something different than all the other MMOs out there
People who enjoy crafting and gathering
That's my 2 cents anyway. Are there better games out there to play right now? Really depends on what you're looking for. If you're looking for a game like WoW, then WoW or LotRO are your best bets. Looking for a sandbox style space-combat/strategy/economic style game? Eve Online is good for that. Looking for great PvP? I've heard great things about Warhammer Online and Dark Age of Camelot in those regards. Eve Online also has fun PvP, though it takes a while to get good enough to compete in PvP. However if you are looking for something that breaks the mold, maybe cause, like me, you've been playing MMOs and other MMO style games (MUDs for instance) for years and years and gamesthat follow the same old mold just can't keep your interest anymore, than FFXIV may be perfect for you, as it is for me. That's not that the game itself is perfect, but given what it does offer compared to the competition, it's the best option out there.
If you're relatively new to MMOs, you may love it or you may hate it. If you're looking for convenience and mindless game play, not that either of those are bad, then you're probably better off playing World of Warcraft or Lord of the Rings Online. Both are great games, but very different from what Final Fantasy XIV is. FFXIV can be extremely fun, but it does require a bit more work to succeed than the average MMO, and certainly more than either of those two I just mentioned.
Hope this helps you make your decision :)