Schema qualification necessary for query plan reuse?
For a plan to be reused all of the attributes in sys.dm_exec_plan_attributes where is_cache_key=1 must be the same. A list of these is below.

acceptable_cursor_options
compat_level
date_first
date_format
dbid
dbid_execute
is_replication_specific
language_id
merge_action_type
objectid
optional_clr_trigger_dbid
optional_clr_trigger_objid
optional_spid
required_cursor_options
set_options
status
user_id


The one affected by using two part names is user_id

If you try the following under the credentials of a user with default schema dbo

DBCC FREEPROCCACHE;

CREATE TABLE dbo.FooBar(X int);

EXEC('SELECT * FROM FooBar');
EXEC('SELECT * FROM FooBar');

EXEC('SELECT * FROM dbo.FooBar');
EXEC('SELECT * FROM dbo.FooBar');


And then execute the following query

SELECT usecounts,
       text,
       value AS [user_id] 
FROM sys.dm_exec_cached_plans
CROSS APPLY sys.dm_exec_sql_text(plan_handle)
CROSS APPLY sys.dm_exec_plan_attributes(plan_handle) AS epa
WHERE text LIKE 'SELECT * FROM %FooBar'  and attribute='user_id'


You will see the following results

usecounts   text                                user_id
----------- ----------------------------------- -------
2           SELECT * FROM dbo.FooBar            -2
2           SELECT * FROM FooBar                1 


This shows that both plans got re-used when the identical statement got run for the second time. The docs for sys.dm_exec_plan_attributes explain for the user_id


  Value of -2 indicates that the batch submitted does not depend on
  implicit name resolution and can be shared among different users. This
  is the preferred method. Any other value represents the user ID of the
  user submitting the query in the database.


This appears to be incorrect! It seems from my testing that the value it actually uses for the user_id in the second case is the schema_id of the default schema for the executing user rather than an identifier for that specific user. Running the four EXEC statements again under a different login with default schema "dbo" gives.

usecounts   text                                user_id
----------- ----------------------------------- -------
4           SELECT * FROM dbo.FooBar            -2
4           SELECT * FROM FooBar                1 


Showing the plans for both versions of the query were able to be re-used between users. Finally running the four EXEC statements again under a third login with default schema "guest" gives.

usecounts   text                                user_id
----------- ----------------------------------- -------
6           SELECT * FROM dbo.FooBar            -2
4           SELECT * FROM FooBar                1
2           SELECT * FROM FooBar                2


Showing that the plan for the dbo qualified query was successfully shared between the users with different default schemas but the non schema qualified query needed a new plan compiled. 

If you don't see this sharing happening ensure that all logins you are testing have the same set_options,language_id, date_first,date_format as these are among the cache keys listed at the beginning and any differences in those  will prevent the plans being reused between sessions.