I was looking to travel so I went and got a Visa, then I Discover(ed) I had overspent on my Mastercard so I did a balance transfer to a new AmEx. Does that count? If the mall has a GameStop, JC Pennys, Sears, NY & Co, Journeys, Bath & Body Works, Gap, and Old Navy do I need every card to use at those stores? I don't care anything for Discover or AmEx. You never know if the restaurant you are eating at accepts either one.
I have not read where network matters for FICO and doubt it would. The card issuer may matter on a manual review for a mortgage, for example if you only had First Premier and Continental Finance as your only CC's it may look bad, but if you had a Chase and a CU it may look better. If you travel to Asia often then as someone said Discover would benefit you. The most important feature isn't the network but this issuer and what the card can do for you. I no longer have Discover, long story but I have AMEX, MC, and Visa. If you do most of your shopping at Costco, you need Visa, the vast majority of others take both MC and Visa. Discover is next in acceptance with AMEX being last. One final thought, look at where you shop most and see what they don't accept, and get that card last if at all.
Of course for a couple of reasons there's a good reason to have 1 of each. Any bank/CU will issue you a V/MC depending on which contract they prefer for pricing on the swipe fees they get to collect. Some banks offer a co-brand AMEX / Discover for the same reasons of the swipe fees. Back in the day neither AX/DS did any co branding with different banks and only issued them on their own. There's a sense of achievement by obtaining some of the single lender cards like AX/DS because of their history of lending UW required to get such cards. As for scoring purposes it doesn't make a difference one way or the other. Scoring all comes down to payments, time, inq's, utilization levels, and debt.
The perk of AX / DS though that aren't cobranded are the SP CLI's on the accounts on a regular basis. Especially for AX where you can exponentially upgrade your CL every 6 months with a SP if your profile supports it. Discover is a little slower but hey they grow with time and can be a little stingy when it comes to some profiles and let the money flow on others. AX isn't a BT card no matter which one you go for and Discover is always offering some deal on taking on a BT.
If someone has v/mc/ax and not discover then I would recommend getting one. If they don't have an amex then I would point them to BCE/ED unless they want to invest annually with a fee. There's a use for any of them just like whatever you have in your wallet currently.
Personal preference is what it all comes down to though in the end. How you use them or other cards in general determines your needs/wants as well.
I'm surprised Discover is highly accepted in Asia. Learn something new everyday I guess.
It's because of their tie in with UnionPay, each working on the others networks from what I understand.