I love playing Brand, and usually do good with him. But he has a lot of weaknesses other than a lack of mobility.
His biggest strength, obviously, is the hp shred. The problem is that he's a burst mage, not so much a poke mage (although he can poke fairly well with his AOE nuke). If there's 2 enemies running at you, the passive isn't going to do that much when you cast everything up front.
His stun is very unreliable. Not only is it a straight line, single target skill shot, but you have to hit them with a previous spell before you can use it. This is a lot of wasted time. So you need to be in range to E them or you have to land W. Being in E range puts you in danger, and W is yet another skillshot. So you have to either be in danger, or land another skillshot before you can cast a second skillshot just to stun them. 
on the other hand, doesn't have as much raw damage as Brand (although she has more reliable burst), but her stun isn't a skillshot, goes off on the first cast (if she properly charges it first), and can be AOE. As you can see, Annie's stun is far, far better than Brand's. Her AoE damage isn't that far behind his with Tibbers up. She has E which gives her a great amount of safety.
His W, E and R don't really do anything. They're just damage. They have no utility on them. Ahri has an incredible CC and fantastic mobilty. Annie can farm mana for free. Anivia has a small AoE stun that has insane scaling (1:1 on both Q and E), a wall, and an AoE slow with her ult. Syndra has a slow on one nuke and a stun/knockback on another. Cassiopeia gets movespeed and has an AoE slow, and an AoE stun. See my point here? Pretty much every mage has some utility on their spells. Brand has one abilty that gives utility: Q.
I think he plays most like Anivia, but without the heavy mana items needed. He has an unreliable stun and great damage, while being slow. The problem here is that Anivia brings a LOT more utility to a team, and her nukes scale extremely well with AP. ALthough she only has two basic nukes, they both have a lot more base damage AND a lot more scaling than Brands. So she can do about the same damage as his entire Q W E combo, with just Q E. But she also has wall. Their passives are both fairly useful, but I would have to give it to Anivia. You can trade 1 for 1 in the laning phase if you have Egg up and gain a disgusting advantage. It's also fantastic late game in team fights if they focus you first. THey're forced to kill a 2k hp egg with bonus armor / mr while your team focuses them.
Another problem with Brand is his ultimate. It's reliant on your opponents being idiots. It's never good when your abilities require your opponents to make a mistake to function properly. His ultimate is REALLY GOOD when you ult someone, and then one of their allies flash in j4 "I'm helping!" style and bounce the ult to them 2 more times. It's really bad when their allies properly move slightly away from each other, and it fizzles out immediately, doing little damage and no side effects.
So all Brand really has is damage. The problem is, his damage isn't really good enough to justify his complete lack of utility. Vlad, Anivia and Ziggs (among others) can easily do as much, if not more, champ damage than him while being safer and bringing more utility to the team. The exception is when the enemy has a lot of HP stackers, like Cho'gath, Zac, and Volibear. In those cases, Brand is fantastic at burning away their hp, especially with Rylais / Liandrys. Unfortunately, most of those champs are also very good at killing him.
, they are both immoblie but at least xerath trades that for mana sustain, skillshots that aren't blocked by minions that have long range and a much more reliable stun
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