I'm reading a commented version of the Enuma Elis and it seems as the Esagil was THE temple in Babylon. They celebrated the yearly festivities in the Esagila and the Esagila is the temple always referred to as 'The House of Marduk' in the different ancient texts.
However, the Etementaki was monumental, so much so that it's the origin for the Babel's tower myth etc. Why isn't the Etementaki the House of Marduk?
Thanks in advance
Have a look at this map by Stefan Maul for Brill's New Pauly. Esagil (E.SAG.IL 'House/temple [with] lofty top') was the name for Marduk's actual temple; Etemenanki (E.TEMEN.AN.KI 'House/temple [of] the foundation of heaven and earth') was a monument to the creation of the world, but it only had a small temple at the top. So at 92 metres tall, Etemenanki was the more visible building, but Esagil was the more important location for ritual activity - it's even mentioned directly in Enuma elish (VI.62 onwards). To confuse things even more, the entire temple complex (Esagil proper, Etemenanki, Zarpanitum's chambers, and the walled courtyard) was often called Esagil.
For those interested, there's a great discussion on Esagil's function in Enuma elish and beyond in Lambert (2013), Babylonian Creation Myths, p. 196-201.