Ok, here's an explanation of the KoF98 Stock Advantage system:
In KoF98, SNK gave up the attitude change based on team relations of KoF97 in favor of a system with more or less fixed attitudes for every chara, plus a random chance of a change in attitude (that goes for all Neo versions of the game), it's just that some charas are more likely to keep a certain attitude than others. For example, Takuma always is angry, at least I haven't seen him neutral, let alone happy in the homecart version.
To see the current mood of your characters, press and hold start at the team order screen.
The attitude changes from fight to fight for most characters. It does so on homecart and NGCD, while on MVS, the attitude changes daily based on the internal calendar, but some characters still have a "preferred" attitude. I guess resetting (not power-cycling) an MVS cab/board will change it as well, haven't tried that.
The attitude system has two functions. First, it determines how likely it is for the following member of your team to help you/do a cover attack (similar to a striker attack in KoF99 to 2k1), and second, it either gives you a power stock bonus or takes one away. A happy chara will always help you, a neutral one may or may not help you, and an angry chara will never help you.
About the stocks bonus/malus: If you lose a round with a happy character, he will give a bonus power stock to your next fighter, plus all power stocks he gained during the round. Say you fight with a happy Chin in round one, gain one power stock and get defeated, then the next team member will get the power stock Chin gained, plus an extra one because Chin is a good guy and wants his team mates do well.
However, if you fight with an angry character, earn two power stocks and get defeated, the next team member will get only one because an angry chara always takes one stock away/keeps one for himself. If you gain only one power stock, the following team member will start out with zero stocks left.
A neutral chara hands over the stocks he gained when he gets defeated, but neither adds nor substracts one from the total no. of stocks.
If you beat an opponent/win a round, you will get no bonus or malus whatsoever and your stocks will increase normally based on the energy you gain from attacks and the amount of damage you receive.