Short and put in lay terms:
There's no standard defined on how to pass this information between apps, so there are no two apps who can interact the way you want.
Longer and with some more detailed information:
The app-selection menu for e.g. a browser or a homescreen only appears when multiple apps announce their being-available for a certain service, and only when this service is called (to put it in easy words; the longer and more technical variant talks about intents and listerners). While web-browsers and homescreens are somehow "generic services" existing on all Android devices, there are standard "intents" defined (see e.g. this question on stackoverflow for opening a page in a browser -- or this question here which probably explains it even better).
As long as there is no corresponding intent (with a defined API for how to pass it the specific chapter:verse to show), your wish can not be fulfilled. Moreover, application developers must implement this into their apps before you can use it.
As to my knowledge neither such API exists nor is it implemented -- there cannot exist any programs acting according to your wishes (except, of course, both are from the same developer; if two or more agreed on terms of how to handle this, that already would mean defining an API).