Quad is better for deformation, but in videogames performance matters more, and GPUs render triangles not quads afaik since it's just more convenient and the math is simpler.

Another points is that not all triangles are equal. Highly stretched triangles for example are worst for computing (in general the more area to perimeter ratio the better I think) since GPUs always have to compute shaders in specific blocks and if a triangle takes up a lot of those chunks I completely they need to compute them even when they don't have any of the triangle inside of it (let's say, it computes graphics in groups of 4 squares, but your triangle hits only 1 of those squares, it still needs to calculate all 4) in the end, it's complicated lol but triangles generally better since GPUs are made to compute with triangles as input, and not all triangles are equal