I did a quick test, and it seems you can compare schema directly:

In [3]: import whoosh.fields
In [4]: WHOOSH_SCHEMA = whoosh.fields.Schema(
  docid=whoosh.fields.ID(stored=True, unique=True),
  doctype=whoosh.fields.ID(stored=True, unique=False),)
In [6]: WHOOSH_SCHEMA2 = whoosh.fields.Schema(
  docid=whoosh.fields.ID(stored=True, unique=True),
  doctype=whoosh.fields.ID(stored=True, unique=False),)
In [7]: WHOOSH_SCHEMA3 = whoosh.fields.Schema(
  docid=whoosh.fields.ID(stored=True, unique=True),
  doctype=whoosh.fields.ID(stored=True, unique=False),
  docfilehash=whoosh.fields.ID(stored=True),)
In [8]: WHOOSH_SCHEMA == WHOOSH_SCHEMA2
Out[8]: True
In [9]: WHOOSH_SCHEMA == WHOOSH_SCHEMA3
Out[9]: False