Postgres: Query to compare Data with previous Data

select
    item_id,
    min(price_cat_a) filter (where rn = 1) as a,
    min(price_cat_a) filter (where rn = 2) as a_before,
    min(price_cat_b) filter (where rn = 1) as b,
    min(price_cat_b) filter (where rn = 2) as b_before
from (
    select
        item_id, price_cat_a, price_cat_b,
        row_number() over (partition by item_id order by checkdate desc) as rn
    from t
    where checkdate <= current_date
) s
where rn <= 2
group by item_id
;
 item_id |   a   | a_before |   b   | b_before 
---------+-------+----------+-------+----------
       1 | 29.99 |    39.99 | 84.99 |    89.99
       2 | 42.99 |    41.99 | 88.99 |    81.99

You can use a lateral join:

SELECT today.item_id,
       today."Price Cat A",
       before."Price Cat A" AS "Price Cat A Before",
       today."Price Cat B",
       before."Price Cat B" AS "Price Cat B Before"
FROM main today
   CROSS JOIN LATERAL
     (SELECT "Price Cat A",
             "Price Cat B"
      FROM main
      WHERE item_id = today.item_id
        AND "Checkdate" < today."Checkdate"
      ORDER BY "Checkdate" DESC
      LIMIT 1
     ) before
WHERE today."Checkdate" = current_date
ORDER BY today.item_id;

These items doesn't exist on every day -- because of this, your original query has an error too (i.e. it won't contain all of your items).

If you are looking for the last (and the second last) checkdate, there is no need to use current_date (unless, there might be future data in your table; in that case just append where checkdate <= current_date to filter them out).

Finding the last row (within its group, i.e. in your case, it's item_id) is a typical greatest-n-per-group problem, and the second last is easy with the lag() window function:

select   distinct on (item_id)
         item_id,
         price_cat_a,
         price_cat_a_before,
         price_cat_b,
         price_cat_b_before
from     (select *,
                 lag(price_cat_a) over w price_cat_a_before,
                 lag(price_cat_b) over w price_cat_b_before
          from   t
          window w as (partition by item_id order by checkdate)) t
order by item_id, checkdate desc

http://rextester.com/AGZ99646