The difference (at least in theory) behind a static Mp5 and % Mana Regen is that obviously the % regen will become much better when the caster is at low mana. Brand has a higher Mp5, so he can stay "topped off" on his mana easier if he is more careful with his spells. However this punishes Brand if he spams his spells too hard. Since Brand is heavily a combo mage, this makes sense. It pushes Brand to think carefully about how he wants to use his mana. When he has an opening, he can drop the rest of his combo.
In early levels, Pre-6, this makes a much bigger difference (until mages can build mana through like a RoA or Tear or just stats, they rely more on Mana recovery/regen)
So Brand, early game, is limited to only a few combos. However, his early damage output is much higher than Veigar, since all of his abilities deal damage and apply his passive burn, where Veigar only has his Q and W (both skillshots, hard to land W without stun) until he gets his Ultimate.
Anyway, what this means is that Veigar's % Mana increase let's Veigar spam his spells early game with fewer mana concerns. Where Brand can stay at higher mana, Veigar can comfortably stay much lower in his mana pool and still have some spells to cast.
Veigar's passive actually gives him more mana regen than Brand as soon as he hits 75% mana. (25% missing mana = ~37% increased mana regen. 6*1.37 = 8.22 at level one)
Another illustration: If they both spam the hell out of their spells and, for the sake of argument, end at like <10 mana. Veigar is going to have ~14+ MP5 where Brand only has 8. So it will take Veigar about 20 seconds to gain enough mana to cast his cheapest spell, where Brad will have to wait about 30 seconds.
Basically, Veigar's passive lets him spam his spells gleefully, which he should be able to do. Especially since Veigar wants to spam farm his Q to get his AP stacking. So he needs that low-manapool regen boost to let him keep spamming.
edit: fixed some math
