I also only play Annie because I like her a lot. She's very simple to play and that's the cost of her being outgunned by so many other harder to play champions that have higher utility. It's very rewarding to be the underdog and come out as the victory. Maybe I am optimistically masochistic. As Annie, I do have tremendous problems with long-ranged. They do as much, if not more damage than me from a safe distance. You can tell by how fast they can clear minions. They also seem to use less Mana for their AOE clears than I have to for my AOE w clears if I max it.
If I max my w, I can keep up with aoe minion clearing but at higher mana costs, but its cooldown is fairly long, and I forfeit any kind of ability to respond to harassment. If I max q first, I can manage mana and cooldowns better and secure minions but only 1 at a time, so farming becomes very slow compared to them taking out 3-4 minions at a time instantly, and it puts me in range to be smacked.
This is from my perspective:
Annie: Has a damage % reduction shield that is mostly only useful versus non-casting physical attackers like ADCs, so I try to support as Annie mostly rather mid where I find maxing the shield first pulls great results when the ADCs go after me. Good AOE clear but only when leveled to at least 3-4 to be effective and but it is higher mana demanding. She has a long range auto attack but the animation time is slow. She has a lock-on single target fireball that can refund mana and cooldown but only on kills, and instant-cast AOE stun with w or ult but only when passive is charged and ult has a range shorter than q and w. Her kit nearly requires the spell Flash to have Annie be most effective, but even then, she is slow moving and if the target has a dash and can know what to expect from an Annie (she is the most predictable character! if an Annie is staying still or moving towards you, you immediately know what she's planning), results in many wasted flash and ult, and makes you look really poor. Most likely death also since you are in the middle of a group of enemies all by yourself for a few seconds. All of Annie's skillset is reliant in some way on one or two other things in order to work to maximum potential, but she is still vastly simple compared to others. She has 3 damage spells, where most others have 4. Her shield is mostly used as a way to charge her stun. For defensiveness I don't think its really that great unless you build defensive MR and armor items too. I like the revenge aspect of Tibbres, only except the AI is a bit ridiculous sometimes. If you are nearly killing someone to 1% hp, but someone else kills you, Tibbers makes a B-line straight for the person who killed you, rather the person with 1% health he was just smacking. Also if you are in a fight with a person with 1% hp, and they kill you at the same time you cast q, your q just disappears and they get to live. These happen to me so often and it really sucks.
vs
Hard Lanes: (requires Jungler help, even tower farming difficult)
Leblanc: The one I most struggle with. She's really, really annoying and very obnoxious because she knows she has the upperhand in engage, doing lots of damage, then disengage. Repeatedly until you are dead. When she sees an Annie mid she just licks her lips greedy. She can rush up to my face, and I have two options: run and only just take dash damage, or attack but get stunned by chains and take even more damage, possibly die
Xerath: His cooldowns are virtually seemingly zero. I can dodge a shot, but he'll have another coming in 2 seconds. It just does not stop.
Orianna: Has HP shield and speed, and aoe. Can stand back really far and still outfarm me due to better scaling long-range AOE, while I have to walk up and take damage to the face in order to take out 1 minion at a time
Syndra: Has aoe stun and knockback, long range aoe, and can use Tibbers against me.
Brand: Has five sources of damage and tons of aoe and damage over time, and a stun.
Boring Lanes: (tower farm only)
Zyra: Have to tower hug. Those plants start to hurt.
Heimerdinger: He can seige your tower right from under you. You can flash ult him but only if he's next to 2/3 of his turrets, but he will never actually put them that close together.
Malzahar: Has invisibility shield and long range aoe and a silence. You cannot come near this guy at all.
Morgana: Has an HP and CC mitigating shield, self-healing, but at least she can't completely drive me out.
Zed: Not a problem for me, I just have to rush Zhonyas. But by that time I will have already died to an ult or two, and he's already down raising havoc in bottom lane while I'm dead.
Ahri: Not too much problem for me, if I can just dodge her pink charm. Buy she can dash to you which is similar to just flashing, and guarantee charm and facewreck me.
Kassadin: Not too much of a problem in the lane, but he is almost always in some other lane deleting my team and I can't keep up with him.
Still, I love Annie and I won't stop playing. I don't know how she can be made to be better, but I don't want to see her changed just for the sake of change and possibly ruin what I love about her: simple, and effective even when behind. A well-placed flash Tibbers can turn some games if another player is fed and can capitalize. Annie with an Amumu or Malphite or Sejuana can do some crazy things together. But if Annie is the team's only initiator or AOE CC, nothing can happen except a dead Annie.
Also, tanks with high damage like Renekton, Nasus, Wukong, Nocturne, Darius, and Garen make Annie cry :(
Can't kill them at all, but they can easily kill you. They laugh as they absorb your whole combo and go from 100% hp to 80% hp, and they do 2-3 hits on you. Nocturne can just keep ulting you all game and there is nothing you can do, even under a tower.