Co-Branded vs. Non-Co-Branded Credit Cards
I see value in being "brand loyal" when it comes to travel. Of course, we might miss a unique family-run experience in Rome or Paris, but we tend to save those experiences for outside larger cities (like, try to find a chain hotel in Maribor, Slovenia). Same with airlines. While our travel destinations usually fall under Oneworld Alliance carriers, we sometimes might need to take flights on local airlines or may find a bargain on another larger carrier. But by and large, we stick to Oneworld airlines. They've treated us well.
Retaining hotel and airline status also remains a high priority for me, as they usually represent a good value in terms of service level/expectation. For example, having "elite" status with a hotel chain means you may get an upgraded room, have a later check-out/earlier check-in time, or get free/discounted food and/or amenities. It also means you earn points at a higher than normal rate, and thus can redeem them sooner (or save up more of them quicker for high-end redemptions). Same thing with airline status: the higher status, the more perks you get, like upgrades, early/free seat selection, and higher earning rates.
Co-branded credit cards were made to reward loyalty, but they're not all created equal. Usually co-branded hotel cards will offer some level of elite status (which comes with its own set of benefits) and other non-hotel perks, but they usually charge an annual fee (sometimes hundreds of dollars). Similarly with co-branded airline cards: while most do NOT offer immediate elite status, they usually offer a fast-track type option to elite status, along with some combination of lounge access, companion certificates, and higher earning rates on certain types of purchases. Annual fees can range from ~$30 to more than $700, so it's important to make sure you utilize most all the benefits a co-branded card offers. Co-branded cards can also have different "levels" – like the Marriott Bonvoy cards: Bevy, Boundless, and Brilliant, where each offers different elite statuses, perks, and earning structures. And annual fees.
You may also see co-branded cards for Amazon, Target, Disney, hotels.com, Costco, etc. These give you (small) perks related to those establishments and they may or may not be worth your time. Generally speaking, if travel is why you're collecting points & miles, stick to co-branded travel cards or non-co-branded cards (NCBC) with transferable points/miles.
You can read about the different co-branded cards we personally use HERE.
NCBCs offer the chance to earn "points" (or miles, confusingly) based on different categories of spending. For example, you might earn 3x points on gasoline, and 5x points on groceries. Or it may be a flat earning rate of 2x points on every purchase. To confuse us, some NCBCs (looking at you Capital One!) earn "miles" redeemable on any airline (so they say). These NCBC cards usually offer incentives to you if you redeem their points (or miles) through their own travel portal. In my experience, however, that can lead to problems if something goes wrong along the way, because you essentially booked through a third-party vendor, and will need to contact them if you need to make changes or have something rectified – the hotel or airline can do nothing for you, even if you have elite status. And that can be frustrating at an airport when a flight is delayed and stress levels are high. Like co-branded cards, NCBCs also offer cards with no annual fees and cards with annual fees (up to almost $700+ in some cases).
While I see the value in NCBs and being a "free agent", I still like (and utilize) the perks of loyalty status that come with co-branded cards. It's nice to check into a hotel and know I will (usually) get very good customer service if I ever need anything along the way. And I usually get treated even better outside the US because those establishments don't see elite status customers as often.
That said, we do have a couple of NCB cards, but these serve as our emergency cards. We keep them because they have no annual fee, and we've had them for a long time, which is important for strong credit scores...