It is difficult to learn from it without admitting that the cards were flawed, the philosophy of both methods led astray. To my knowledge, I do not think that the experiment was reproduced. In any case, it was not documented.
Anyway, it is clear that both methods are totally incompatible. The Balanced Scorecard is an interventionist method. It is based on a behavioral and centralizing tendency principle trying to simplify the complexity in a formal approach of exhaustive causality.
The GIMSI method is a cooperative approach focusing on a smooth integration in an ambient complexity. It is based on a simple and natural accountability, autonomy and communication of all players, full decision-makers. The three features are inseparable.
Each decision-maker is a point of mastering complexity. The Balanced Scorecard method only works in a pyramid and hierarchical scheme. GIMSI method is more suitable for "flat" cooperative-type structures, encouraging initiative and lateral exchanges.
As a last remark, it is recommended to the enthusiasts of the Balanced Scorecard methodology not to let themselves be too much forward led by the orthodoxy of the designers.
Thus, it may be a good idea to associate a particular interest in areas that are not differentiated in the method, taking place however at the forefront in the chain of value creation, such as the network suppliers, information system or the importance of the opinion of the public (weight of ethics), as well as the related concepts of the sustainable development.
For many companies, competitive advantage is directly dependent on the care attached to these areas. By not differentiating them, it is simply impossible to build these winning strategies.