The quick answer
Round pools fit more yards, cost less for the same water, and are easier to set up — great for cooling off and family play. Rectangular pools are better if you actually want to swim lengths, and they look more like a traditional pool, but they need more space and careful leveling.
Space & installation
A round pool distributes water pressure evenly, so the structure is simpler and quicker to assemble. Rectangular pools have more engineering at the corners and demand a perfectly level base — worth the effort if lap swimming matters to you.
Swimming experience
If you picture swimming actual laps, go rectangular and prioritize length. If the pool is mostly for lounging, games, and kids, a round pool gives you more usable water per dollar.
Cost per gallon
Round pools generally give you the most water for the money. Rectangular pools cost more for the same volume because of the added structure — you're paying for the shape and swim length.