TL;DR. Two flagship no-fee flat-earn cards. Freedom Unlimited earns 1.5x on everything (3x dining, 3x drugstores, 5x Chase Travel). Double Cash earns flat 2x on everything (1% when you buy, 1% when you pay). Standalone, Double Cash wins on simple cash-back math. Paired with a Sapphire Preferred or Reserve, Freedom Unlimited converts to transferable points, which usually wins on redemption value at scale.
The three dimensions that actually decide it. First, raw cash-back rate. Double Cash's 2x flat beats Freedom Unlimited's 1.5x flat. Second, pairing potential. Freedom Unlimited's cash back is actually Chase Ultimate Rewards points (1 point = 1 cent) and combining with a Sapphire card unlocks transfer partners (United among them; for World of Hyatt, Chase states 4:3 for Sapphire Preferred cardmembers and no Hyatt rate for its Sapphire Reserve cards). Double Cash's earnings arrive as Citi ThankYou Points, which transfer to Citi's airline and hotel partners directly at 0.7 of the premium ratio, and at the printed ratios once the points sit on a Citi Strata Premier or Strata Elite account (annual fee). Third, category bumps. Freedom Unlimited adds 3x dining and 3x drugstores; Double Cash is pure flat.
Real customer scenario for each. If you have a Sapphire card and want to earn transferable points on non-bonus spend, Freedom Unlimited's 1.5x converts to 1.5x Ultimate Rewards points, which often redeem for 2 cpp or more through transfers, an effective 3% return. If instead you want pure simple cash back and do not want to deal with a Premier card, Double Cash's 2% flat is the cleanest option.
The trap to avoid. Treating these as standalone cards. Freedom Unlimited's superpower is the Sapphire pairing. Without a Sapphire, it is a worse Double Cash. Without a Premier, Double Cash points transfer at 0.7 of the printed ratio, so treat it as a 2% cash-back card with a modest transfer upside.