AA
I would use Access mate (I'm assuming that you know the basics here). Import the two lists into separate tables, then create a new query which contains the company name fields from both lists. Create a relationship in the query design grid between the name fields of tables A and B using type 'Include all records from B and only those records from A where the joined fields are equal '. In the 'criteria' field under the company name field from B specify 'Is Null'.
Then simply run your query. The results displayed will be those records that exist in list B that do not exist in list A.
The beauty of this method is that as long as you save the query, and even if you subsequently update either or both lists (within Access, either directly or by importing the revised info) then it will still work as advertised.
Sounds complicated, but in practice should take no longer than a few mins.
Gadget 
Feel free to PM me if you would like any more help.