I don't know this for sure, but I can't imagine card network diversity matters very much, if at all. Card issuer diversity can matter a bit, but mostly to make sure you aren't putting all your eggs in one basket in case a particular bank decides you are too much of a risk for whatever reason and kills your limits and/or closes your accounts. Amex and Discover are also issuers, so there's certainly no harm in diversifying with one or both of them, but having all your cards at Capital One or Chase, for instance, is more of a problem.
That said, each network has its own pros and cons. So, get the cards you want based on what they offer, including the issuing bank and card network benefits.
