Similarities between #usecases & #epicuserstory YES! But they are not the same. #agile #userstories more granular than Use Cases.
Typically a Use Case will have many Functional and Non Functional requirements that trace to and are realised by a Use Case. The use case records the interaction between the User and the System and main and alternative paths through the taskflow are documented. This can make them quite large and certainly a lot bigger than a few days to develop a single use case. The old design rule of "one person, one place & one time" helps to design use cases to be at a similar level of granularity, but still much bigger than a single user story.
On the other hand a user story must be small to meet our INVEST mnemonic, S standing for small. So definitely not similar to a Use Case. You could say that an Epic Story, a big story that can be broken up into lots of smaller stories, could be similar to a Use Case in granularity. When modelling a Use Case we have main flow and Alternate flows and when modelling User Stories we would have a separate story for each flow.
If we had to compare something to traditional requirements analysis you could say that user stories are more similar in granularity to a functional requirement. But even functional requirements can be bigger or sometimes smaller than a User Story.
I personally wouldn't try and compare the two directly. They are used in different ways for different approaches to capturing requirements. A professional knows which tools is the right one for the job. You don't use a screwdriver when its a job for the wrench. Depending on the type of project approach and the level of detail needed and when, choose the right analytical tool for the job. We all have our virtual kit bag of tools and techniques. Get good at identifying the right ones to use and when to deliver the best outcome for the business that is paying you for your time and experience.