The arguments against special characters are:-
1) They are too well known by the enemy who will be well aware of all their strengths & weaknesses.
2) They are expensive because you may pay for attributes, items, special rules that you might be unlikely to be able to use during the game - possibly because of the enemy's type of army.
3) They don't fit into your tactical plan.
I am not however of the opinion that special characters should always be excluded - even in tournament games.
Here are my reasons :-
1) Special characters often have access to abilities that cannot be replicated by customising your own character - take the High Elf Teclis for eample, he knows every spell in the Warhammer World. You have to choose a Lore of Magic before the battle but he still knows all 6 spells.
2) Some special characters give you a combination of items that cannot be repeated through customisation because a similar combination would exceed the maximum allowable points value for magic items.
3) Some characters are outrageously tough or useful. Take Grimgor Ironhide for example. Or the leadership qualities of Settra the Imperishable or the the unique Army composition that Skrag the Slaughterer gives you access to.
4) Characters have history which is great for the battlefield banter :)
I am not particularly keen on tournaments, I'm always too worried I'm meet a rules lawyer or someone who can't bear to lose. They can easily wreak a game for me. I prefer to play amongst friends with some friendly banter, a pizza and a few beers. Because of that I usually take at least one special character particularly is they have got a 'lot of previous' against the enemy army.There's nothing like building on that 'previous' until your enemy will do anything in the next battle just to kill your character.
I guess it all depends on what kind of game you want to play. In a lot of serious competition situations you might benefit from customising your own characters to give you the benefit of suprise. I guess it's also a bit more fulfilling to win a battle with all your own tactics and characters.
The choice is yours, I'm split 50/50 on this one :)
