My daughter was in the exact same position as you - deciding between these 2 schools for Psychology. She has decided on Trinity after multiple visits to each school and the surrounding area. Southwestern was the front runner until recently. They are both fantastic schools, but a big part of the decision was imagining her life outside the classroom/campus. Georgetown is a very small little town near the Southwestern campus, with a very Republican/Texas vibe. Going to the same few stores over 4 years might get boring, and Austin is realistically just too far for frequent visits. Southwestern also has a smaller campus and student body. The area around Trinity felt more modern/cosmopolitan. The Pearl area, 5 min drive south from campus, has a great selection of fantastic restaurants. The Quarry area, about 7 min drive North from campus, has everything a young adult needs - cinema, and a plethora of stores from Loft, Nordstrom rack, ulta beauty, starbucks , whole foods, and the list goes on. There are also many other bars, restaurants etc in the local area as well as the river walk.
Trinity is indeed about 80% Texan as someone mentioned, but Southwestern is closer to 90%. Also, Trinity will get more National recognition soon, as it has been reclassified as a National LAC. The new ranking will be revealed in US News Fall 2022, and the expectation is that it will attract more talent from OOS.
Good luck in your decision!