I am very interested in comparing the architecture between these two civilizations. It seems they are both famous for having these pyramid structures, and to me they seem largely similar. So what is the difference between these two civilizations in their architecture?
I say this often, but this is a difficult question to answer. I'd say there are two main reasons. One is that the Maya civilization wasn't united under a single political structure, or one that might create a uniform architectural tradition. So pyramids in places like Uxmal can look very different from those in Tikal, and both might look nothing like a temple in Dzibilchaltun. The second thing to consider is that Mayan society has lasted on incredibly long time: there were large Mayan cities by 750 BCE, and the last independent Mayan kingdom only fell in 1697 (and of course Mayan communities thrive today, some with pretty autonomous power). So, there are gigantic ancient 2,000+ year old structures like El Mirador's El Tigre, and more modest ~700 year old structures from Mayapan that are both from the Maya civilization.
But for all their variation, it's true that Mayan states were a constantly interacting set of Mesoamerican groups which had more in common with each other than with peoples like the Aztec. So your question is an interesting one. Let's finally look at it! Most of what I write will be pointing out specifically Mayan characteristics. Also, much of what I write will be about things that intersect architecture with city planning, since I found it easier to compare Aztec to Maya through that combination.
One distinctive formalized feature of some Mayan sites - namely, cities from the southern lowlands - is the so-called "E Group" (the classic example of which is diagrammed here). This architectural organization type's importance
"was less based on their function as observatories as on their social function. While it is likely that the initial complexes built in the Terminal Preclassic period at Uaxactun and Tikal were designed to be functional ob servatories, the continued use and modification of the Mundo Perdido complex at Tikal became a defining element for Early Classic elite and royal lineage."^(1)
The same paper also links E-groups to Mayan "Triadic Groups," another building organization plan widespread throughout the Maya world. Many communities moved away from E-groups to triadic groups, which is "a general term for groups of buildings that consist of a larger central building with two smaller buildings facing each other and positioned in a triangular arrangement vis-à-vis the larger building."^(2) Here are some different variations of triadic groups. This style lasted for some 1,500 years, and probably had specific meanings behind its organization, although those meanings are unclear.^(3)
I'll quote a final author on the a series of characteristics of Mayan architecture. Many of these characteristics were also used by other Mesoamerican societies - for example, the Aztecs certainly made use of limestone - but in combination they are representative of early Maya traditions which continued to be developed throughout their history:
Rather than beginning with explosive episodes of earthen platform building, the Preclassic Maya excavated to bedrock and leveled spaces; they worked with limestone in various forms, from blocks, to chalky dust, to processed stucco; and they mimicked the design and construction of living spaces in monumental, nonresidential buildings and places...Monuments grew from cooperative building that drew inspiration from households and preexisting kin group practices.^(4)
I can also point to at least one distinctively Aztec architectural practice. Aztec city centers were unique in regularly exhibited pyramids topped with double temples, such as in the style of the central Huey Teocalli temple of Tenochtitlan, the Aztec capital. ^(5) This style is absent from the Maya world. Here's another example of a double-temple pyramid in an Aztec city.
Finally, I'll write about an example of something that was clearly different between Mayan and Aztec cities: markets. The Aztec world was one full of huge market spaces, and the government built areas expressly designed for this purpose. Aztec markets
"were usually located in the town center, at least in the larger communities, and had constricted access points...courts [and other non-trade services in markets] seem to be associated with permanent structures...Aztec marketplaces reportedly had a shrine and marker located within the plaza...Structures to house itinerant merchants also have been noted."^(6)
There are even firsthand Spanish accounts which describe the impressive planning of Aztec markets. But Mayan markets were probably a very different affair. Although a few Mayan markets have been found, and some exhibit central planning and structures like courts, they were probably not as architecturally built up or organized as their Aztec counterparts. This may in part be due to Mayan marketplaces possibly being located in central plazas that left little trace, but that would still be relevant to your question of architectural difference. Whatever the case, Mayan marketplaces were built in less permanently visible ways than Aztec ones.
^(1) Guderjan, T. (2006). E-GROUPS, PSEUDO–E-GROUPS, AND THE DEVELOPMENT OF THE CLASSIC MAYA IDENTITY IN THE EASTERN PETEN. Ancient Mesoamerica, 17(1), 97-104.
^(2) Doyle, J. (2017). The Architecture and Spaces of the Early Ajaw, ca. 300–1 BC. In Architecture and the Origins of Preclassic Maya Politics (pp. 71-108). Cambridge: Cambridge University Press.
^(3)]zymański, J. (2014). Between death and divinity. Rethinking the significance of Triadic Groups in ancient Maya culture. Estudios de Cultura Maya, 44(44), 119-166.
^(4) Doyle, J. (2017). Mesoamerican and Maya Monumentality, Identity, and Politics. In Architecture and the Origins of Preclassic Maya Politics (pp. 26-36). Cambridge: Cambridge University Press.
^(5)https://open.library.ubc.ca/cIRcle/collections/ubctheses/24/items/1.0228255
^(6) Shaw, L. (2012). The Elusive Maya Marketplace: An Archaeological Consideration of the Evidence. Journal of Archaeological Research, 20(2), 117-155.