What do you like best?
Ellucian has a huge footprint in the industry, and there are talented consultants available to help with implementations and upgrades. (Which is necessary, because the product is sprawling, and new customers will NOT be able to manage it on their own.)
There's also a strong community of users who help support each other. Ellucian offers a user community, but an unofficial one is also very vibrant and technically advanced.
What do you dislike?
They are slow to innovate, they're years behind on certain announced ship dates (e.g., finally retiring Self-Service Banner 8), the support isn't great, they often ship buggy code, and the support site goes down for no reason. Their web portal product (Luminis) is pretty stale. Their mobile solution isn't nearly as good as the one from Modo Labs.
What problems are you solving with the product? What benefits have you realized?
It brought us in one leap from a mainframe onto the Internet, which was huge in 2003. It stores and indexes all of our academic records from all years, and lets us interface with other software, which is an amazing way to extract the latent value in that data.