I think it depends on what you're looking for from the card. For me, the only Discover categories that matter overlap with the Chase Freedom card. But I live in an apartment, so when Discover gave 5% back for home improvement, that was worthless for me. A homeowner in the market for a new lawnmower would have found the Discover card worth it at that moment. Last year I maxed out the restaurant category on my Chase Freedom, but I did it at the end of the quarter, so Discover wouldn't have offered me anything extra. (Note that for me Chase Ultimate Rewards points are more valuable than cash back from Discover because I have the CSR, so I choose Chase over Discover for purchases when they overlap... without the CSR/CSP, Discover cash back is technically more valuable because you can usually buy gift cards at a discount).
Discover always has 0% 12-month balance transfer offers (and 4.99% 18-month offers), which is how I tend to take advantage of my Discover card. Balance transfers aren't for everyone or every purchase, but I find a way to make them work for me on certain large purchases (the key, in my mind, is to develop a payment plan and stick to it before using another one).
Discover tends to let the credit limits grow more frequently than Chase and without hard pulls. With Chase, as long as you're going to be getting a hard pull for a limit increase, you might as well sign up for a new card and get a signup bonus (unless you truly don't want/need a new one). Also, from what I understand, Chase is not at all likely to allow an APR reduction, but Discover will. On the flip side, depending on what places you go to, you may find it more difficult to use Discover. One of my favorite Vietnamese places nearby only takes MasterCard, VIsa, and Amex. Another one only takes MasterCard and Visa. But most major places will accept Discover.
At the end of the day, it probably doesn't hurt to give it a shot to apply. You know your credit profile best. If you believe you're in a good place to be approved, then it's an extra, no-fee credit card that can potentially add value in your life. But if you don't see a place for it in your life, then move on. It's a good card (particularly for the first year), but it's not the only good card out there.
