The advantage of EWS over EAS is mainly in costs:
EWS is included in the MAPI license and is available to all users (like MAPI), so it has no additional cost if you already use MAPI/EWS.
EAS is an ADDITIONAL annual license that goes to blocks of users (25, 50, 100, 150, 200, 250, 300, etc...) and therefore has two disadvantages:
1 - it costs more (and not a little...)
2 - it must be managed user by user if you don't want to waste licenses (so it also costs management time)
3 - EWS supports read-only shared folder syncing, while EAS doesn't