Brand outmatches Veigar in almost every way.

Brand's passive is basically a miniature ignite. In fact, it could be more than an ignite if someone is tanky enough to have 8% of their health do anywhere from - what? - 50-400 damage. (Note: Can't technically outmatch it because it has nothing to do with Veigar's passive. But it is fucking OP, especially considering Veigar only generates extra mana in which Brand really doesn't need because you're dead before he runs out anyway.)

Brand's Q has a lower mana cost and just 1 second longer cooldown than Veigar's, plus its lock-on instead of a skillshot. If target has his passive on it, then it also stuns the player, making a TARGETED stun rather than a stun that can be easily avoided if you're smart enough not to walk or dash into it. Plus it has more range than Veigar's E.

Brand's W has the same cooldown as Veigar's at rank 1, but is two seconds more by rank 5(Brand's cooldown stays the same). His W is also the same area of effect range, same range to hit it at, and it takes less time for it to activate meaning its a ton easier to hit.

Brand's E. My hell. Instead of being a stun, like he has on his Q anyway as a lock-on rather than a 'can-I-land-this-directly-on-top-of-you-or-are-you-even-stupid-enough-to-walk-into-it', he instead gets a second, barely-less-damaging Q that if the target is ablaze, spreads to other targets for more waveclear and teamfight ability!

Brand's R. Again, spreads to everyone for team fight ability and does a FUCK TON OF DAMAGE.

What's that you say? Brand does less damage than Veigar? AHAHAH BECAUSE IT MATTERS, HE BURSTS YOU DOWN TO A PULP ANYWAY! So what, he can't destroy tanks like Veigar? It doesn't matter, he already bursts down every fucking squishy in a team so that his entire team can focus down the rest of the tanks.