Comparing two columns for match, then listing and performing calculation

I have two sets of data; they contain a product number, description, and a cost. They are currently on separate sheets (Sheet1 and Sheet2), but they can be copied to the same sheet if necessary.

Product Number	Description	Cost	|	Product Number	Description	Cost
90001	Item 1	34.99	|	90001	Item 1	31.99
90002	Item 2	17.99	|	90002	Item 2	16.99
90003	Item 3	9.99	|	90003	Item 3	11.99

Effectively, I want to:
1. Check if the product number from set 1 exists in set 2.
2. Return the product numbers that match and each cost.
3. Calculate which is cheaper. (Obviously if it's able to pull the matches and their costs, it'd be simple to do the calculation in an adjacent cell afterwards)

The 1st list has almost 16000 items, and the 2nd is just under 13000.

I've tried tinkering with vlookup, match, index, etc.. and haven't had luck getting things to work properly. Even just highlighting duplicates to try and filter leads to highlighting numbers that aren't duplicates or missing duplicates that I can plainly see.

Any help would be greatly appreciated.