How to determine who is the PI and who the co-PI? Suppose I submit a grant application with other investigators. The application form has one "PI" and some more "co-PI"-s. 

Is it important who of us is the "PI" and who is the "co-PI"?
E.g., is being a "PI" like being a first author on a paper, which (in some disciplines) is considered more highly than being a second author?

Is there a common way to decide who gets to be the PI and who the co-PI, e.g., by alphabetic order of surnames (like the author order in some disciplines)?
There are some significant issues that may influence the selection of a PI versus a co-PI or co-I. There are grants where eligibility requirements may vary, depending on whether someone is a PI versus a co-I. For instance, some programs may have a requirement that an investigator may apply for only one grant as a PI, but could act as a co-investigator on multiple proposals. 

In addition, the PI will likely have additional reporting requirements or be responsible for ensuring the coordination of reporting for the entire team. 

There might also be "programmatic" reasons for selecting the PI—for instance, if the program is designed to particularly support a particular kind of institution, having someone from that kind of institution as PI could be useful.

But, in general, there are so many different programs that, in the absence of more specific information about the program, it's hard to give any kind of general guidance about how to select a PI.