You will not get different query execution plan per user if you don't specify schema.

Unless your system is designed in a such way (it's very rare case actually) that one group of users have a dedicated default schema and all relevant objects are duplicated in every such schema, it is always good idea to specify schema name.

1. It explicitly suggest which schema the object belongs to

2. Because of #1 you will get some performance benefits as compiler doesn't need to check which schema the object is from.