In what major ways did the Greek and Roman religions differ?

First, you have to remember that there is no such thing as "Greek religion" or "Roman religion". Without any real notions of orthodoxy or doctrine in general, both were in reality a wide variety of local religions that formed a continuum more than two separate entities. Now, since about the sixth century BCE Italy as a whole was heavily influenced by Hellenic culture, and Rome was no exception, so there are quite a few ways that Italian religious practice converged with Hellenic, particularly as we travel to the end of the first millennium BCE, and most particularly in expressions of religion most likely to survive: literary texts and religious iconography. Certain differences in these persist (Italian temple forms had certain differences, the presentation of some gods such as Mars/Ares and Saturn/Uranos were quite different) but by and large the Roman/Italian elite had quite deliberately created a set of religious forms that are very similar to what was in Greece.

Now, in terms of ritual practice there are certain observable distinctions, but the problem with using these is my first point, that the variation in ritual practice within the Greek and Roman worlds is so great that we can't really responsibly construct a Platonic form. Ritual in Rome had distinct differences from that of Greece, but so did Boetia. Still, if you want a fun source on this, check out Plutarch's Roman Questions and Greek Questions, where he explains certain mundane oddities about Greeks and Romans to a hypothetical outside observer, and a lot of these have to do with everyday ritual and festivals.