Tangalle and Mirissa are both on Sri Lanka's south coast and are sometimes treated as interchangeable options on a longer itinerary. They are not interchangeable. They are genuinely different places that suit different travellers, and putting them in competition with each other makes more sense once you understand what each one actually is.
Mirissa is the busier, more developed town. It has whale watching from November to April, a well-known beach, Coconut Tree Hill, bars and restaurants along the beachfront strip, and a steady stream of travellers year-round. The sea at Mirissa is good for swimming in the dry season. The atmosphere in the evenings is social and can be loud depending on where you are staying. Mirissa suits people who want an active beach town with a clear wildlife activity to anchor the visit.
Tangalle is quieter, wilder, and less developed. The beaches east of Tangalle town are long sweeping arcs of sand that are almost entirely uncommercialised. The sea here is often too rough for swimming but is impressive to walk along. Rekawa Beach, close to Tangalle, is one of the only places in the world to watch leatherback turtles come ashore at night to nest, from April through September. The town of Tangalle itself is a real Sri Lankan market town rather than a tourist strip. Accommodation options lean toward small guesthouses and a handful of boutique properties set back from the wild beach.
Who each one suits. Mirissa suits first-time visitors to the south coast who want a recognisable beach holiday with the whale watching season as the highlight. Tangalle suits travellers who have done the busier towns and want something with space and a different pace, or anyone coming specifically for the turtle nesting experience.
The two work well as a sequence rather than an either-or. Most south coast itineraries that cover more than a week naturally pass through Mirissa on the way east and arrive at Tangalle a day or two later. Spending more time in one and passing through the other is the practical approach. If you only have time for one, the question is whether you want the whale watching and the beach bar atmosphere of Mirissa or the empty beaches and genuine quietness of Tangalle.