Both Unawatuna and Mirissa appear on almost every south Sri Lanka itinerary and both get oversold in different ways. Here is an honest comparison.
Unawatuna is closer to Galle and more developed. The bay is sheltered and good for swimming. It has dive operators, beach bars, guesthouses at various price points, and a relaxed if slightly rowdy evening atmosphere. The side trip to Jungle Beach is genuinely good. The Japanese Peace Pagoda on Rumassala is a calm half-morning. Unawatuna works well as a first or second stop on the south coast for people who want a beach near Galle without going further east.
Mirissa is further east, about 40 minutes from Unawatuna, and its main draw is whale watching. Between November and April, blue whales pass close to the shore off Mirissa and the morning boat tours are one of the most memorable wildlife experiences in the region. Outside whale watching, Mirissa has Coconut Tree Hill, Parrot Rock, and Secret Beach. The main beachfront strip is busy and the restaurants there are expensive for what they are. Mirissa has more of a party atmosphere in the evenings than Unawatuna.
Which one to choose. If whale watching is on your list and your dates fall between November and April, spend a night or two in Mirissa specifically for that. If you are not doing whale watching, Mirissa is a good afternoon day trip from Weligama rather than a separate overnight stay. Unawatuna is more worth an overnight if you want a beach close to Galle and do not want to go all the way to Weligama.
Most travellers do not need to choose one over the other. The coast is compact enough that Unawatuna can be a stop on the way from Galle to Weligama, and Mirissa can be a day trip from Weligama the following day. Trying to base yourself in Mirissa as the main stop on a first visit and using it to explore the whole coast in either direction tends to work less well because the town has limited transport connections compared to Weligama.