I'm taking an intro class and read that they exchange sequences daily so in terms of data they are equivalent but each site has some differences with regards to features and built-in programs.
What are the main differences, pros and cons?
NCBI and EBI are institutions that provide multiple sequence data resources. You'll have to be more precise about which ones you're interested in. Since you also mention DDBJ, I assume you mean NCBI's Genbank and the European Nucleotide Sequence Archive (maintained by EMBL-EBI). The ENA/DDBJ/Genbank is an international collaboration to share nucleotide sequences so that all have the entire data set under a common file format.
The differences are in the data access methods, e.g. different APIs.
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