Kobo -- can organize collections from calibre. Can customize the layout -- fonts, margins, etc. Has lousy dictionaries, and if you ever need to deal with customer service, it can apparently get extremely frustrating.
Kindle -- stable and simple. If it works, it works very well. On the rare occasion that I have needed customer service, Amazon has been a pleasure to deal with. The store Just Works, and the prices are usually a little better than Kobo. Limited to no customizability (unless you jailbreak, which is hard now) but the defaults suit many people perfectly. However, it is a dealbreaker for many others.
You can email your old books to your Kindle as PDOCs, and they will sync with annotations across all your Kindle devices/apps.
Something to consider... where do you plan on getting books from, going forward? For new books, being able to sync them directly on the device is something very nice to have.
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