Actually, the companies have very different design approaches. Boeing has kept each generation nearly unchanged. So all 737-400s are nearly identical, same with the 737-800. Early, late build, practically carbon copies. Airbus in contrast has kept the model designation unchanged from launch (first flight in 1987) until A320E program in 2006, and then another big change with the neo. In contrast with Boeing, Airbus made incremental improvements/changes in the aircraft (the biggest ones being the A320E program and then neo) so that say a 1990 build is less efficient, with higher fuel burn, than a say 2000 or 2010 build. Airbus has more of a Japanese approach of incremental design improvement.
That said, the fundamental architecture of the Airbus plane is unchanged, while that of the MAX has little resemblance to the original 737-100. The main reason for this is two fold. First, the original A320 has a much more modern design that was not low to the ground, and second the A320 was the maximized base design. The A321 is a stretch, and the A319 is a shrink. In sharp contrast the original 737-100 model was a short range (1500 nm) aircraft seating 74. The 737-200 (seating 110) was a stretch for UA, and then the
737-300/700 was a double stretch, and the
737-400/800 was a triple stretch, and the 737-900 was a quadruple stretch, and the Max10 is a quintuple stretch.
To give some idea of the contrast, the originally designed 737-100 was 93' long, the MAX 10 is 143.7' long. In contrast the A320 is 123' long, with the A319 shrink being 12' shorter, and the A321 stretch being 23' longer. So far less change from the base model.