My impression of the EIS movement is that it was primarily focused on monitoring, rather than execution, types of applications. Using an EIS application to "roll up" performance measures from several different systems, replacing intermediate ranks of middle managers whom used to do the "consolidation". In this fashion, the executive would be able to receive the information when they requested it rather than "when it was ready". This efficiency implied the executive would also be able to review information more frequently. The invevitable filtering by middle managers would also be removed eliminating the influence of personal agenda's on the numbers.
Neither our internal EIS systems nor the research reports reviewed mentioned any thing about execution of actions based on decisions made with the information. In this sense it was one way flow. There were some reports regarding Executive Expert Systems which went the next step and made some decisions automatically based on incoming data but even those did not indicate a flow of action from the executive back into the system and organization.
The EIS in our company is certainly not based on standards. The reason it was a necessary project is precisely because there were heritage systems, without any standards, that needed to be tied togethor. So I don't understand your reference to applicability of standards to EIS, I have more an impression of a patchwork approach (unfortunately).
Enterprise Integration on the other hand is about helping the enterprise function, not just monitoring its performance; EI is about omnidirectional flow of data and execution of actions rather than unidirectional flow to the senior executives; EI can be based on standards (at least at the lower levels) and probably market dominant proprietary open architectures for higher levels in the system. The focus of EI is on empowerment of the worker rather than the Executive.