Embedded enum sets are supported and are fast (but I am not sure to which classes you want to compare them).
Currently you should declare the fields as Set<MyEnum> rather than EnumSet<MyEnum> - otherwise you will not be able to see the enum set values in the Explorer (but you can instantiate it as EnumSet<MyEnum>).
JDO/JDOQL (single string) query for example:
SELECT FROM MyEntity WHERE this.enumSet.contains(:arg)
JPA/JPQL query for example:
SELECT e FROM MyEntity e JOIN e.enumSet item WHERE item = :arg
ObjectDB Support
ObjectDB - Fast Object Database for Java (JPA/JDO)