Upvote:1
Passport are replaced (and get lost), so travel history is not so important. But keep a photo of passport, visa, and stamps. This could help you in future to find out your travel history for new visa applications.
Just it will confuse officers if you give a passport without the entry stamp, or a passport without the exit stamp of the nearby country (e.g. if you are traveling by car).
I would use only one passport per travel (and the other will remain home, so you will not lose it). And possibly I would use the same passport for similar travels, and not to mix them on "enemy" countries. [So US and Israel possibly in a passport and Arabic states in an other].