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 (Hyatt, United). Double Cash's earnings become transferable to Citi ThankYou only when paired with a Citi Premier (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 maxes out as a 2% cash-back card.